English (Compulsory) For Class IX - Unit 1 - Ethics Character builder - Questions And Answers

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The Last Sermon Of Holy Prophet (P.B.U.H)

Questions And Answers

Q.1: When and where was our Prophet (P.B.U.H) born? What tribe /family did he belong to?
Ans: Our beloved Prophet Muhammad (صلى الله عليه وسلم) was born in 571 A.D. in Makkah, Saudi Arabia. Some historian say that he was born in 570 A.D. He belonged to the noble family of Quraish.

Q.2: What did the Quraish worship or believe in? What did the Holy Prophet (صلى الله عليه وسلم) ask / say to them?
Ans: The Quraish used to worship idols and did not believe in one God. The Holy Prophet (صلى الله عليه وسلم) asked the Quraish not to worship their false gods. He told them that he was the Prophet of Allah and asked them to accept Islam and to worship the One and only true God.

Q. 3: What was the reaction of the Quraish to the Holy Prophet's (صلى الله عليه وسلم) preaching? Why did the Quraish oppose them?
Ans: They opposed this new faith, and most of them refused to accept Islam. They thought that he was against their gods and their ancestors. They wanted to go on worshiping idols and did not believe in one God.

OR

Q.3: How did the Quraish treat the Holy Prophet?
Ans: The Quraish thought that the Holy Prophet (Peace be upon him) was against their gods and their ancestors. They wanted to go on worshiping idols and did not believe in one God. So they opposed this new faith, and most of them refused to accept Islam.

Q.4(a): Why did the Holy Prophet (صلى الله عليه وسلم) ask the believers to migrate to Madina?
Ans: Most of the people of Makkah refused to accept Islam. They opposed this new faith so much that the Holy Prophet (صلى الله عليه وسلم) had to ask the believers to migrate to Yathribs, a city 320 km (200 miles) north of Makkah, as they were in great trouble and agony in Makkah.

Q.4(b): Why did Prophet Mohammad (peace be upon him) migrate to Medina?
Ans: With time, as many people started accepting his message and converting to Islam, the Quraish became more aggressive and started making attempts on his life. Hence, when Prophet Muhammad (صلى الله عليه وسلم) got positive signals from Yathrib, he also decided to emigrate there.

Q.5: What is meant by Hijra? Where did it take place?
Ans: Hijra means to migrate to a safer place for the safety of life and faith. The bitter opposition or Quraish and their aggresiveness caused the Holy Prophet (صلى الله عليه وسلم) to migrate to Yathrib (Madina), a city 320 km (200 miles) north of Makkah. He (صلى الله عليه وسلم) left Makkah and stopped at a place called Quba, he (صلى الله عليه وسلم) built mosque there on 28^th June 622 A.D. and then On 2^nd July, 622 A.D. entered Yathrib. This event is known in history as hijra. It marks the beginning of the Islamic calendar.

Q.6: At the time of arrival of Prophet Muhammad (صلى الله عليه وسلم) in Madina, which groups of people used to live there?
Ans: At the time of arrival of Prophet Muhammad (صلى الله عليه وسلم) in Madina, the city had four broad groups of people.

• There were the Muslims; including those who were from Madina and those who had emigrated from Makkah.
• Then, there were the hypocrites; that is those who embraced Islam in name only, but actually were against it.
• Additionally, there were the people from Aws and Khazraj tribes, who were still pagans but were likely to accept Islam.
• Finally, there were Jews, who were huge in number and formed an important community there.

Q.7: To ensure that people of Madina live in peace, what did the Holy Prophet (صلى الله عليه وسلم) do for that?
Ans: In order to ensure that all groups of people in Madina lived peacefully with each other, Prophet Muhammad (صلى الله عليه وسلم) invited the leading personalities of all the communities to discuss that matter. He wanted the different groups to reach a formal agreement for harmony among the communities and for the security of the city of Madina. He succeeded in drawing up the Constitution of Madina, also known as the Charter of Madina, through which a kind of understanding was developed among all the communities living in Madina.

Q.8: What were mentioned in the Charter of Madina? OR What are the three main points of Charter of Madina?
Ans: The three main points of the Charter of Madina were :

• It was mentioned the rights and duties of the Muslims and the Jews of Madina, gave freedom of religion.
• And prohibited any alliance with the outside enemies.
• It also declared that any dispute would referred to Prophet Muhammad (صلى الله عليه وسلم) for settlement.

Q.9: What steps did the Holy Prophet (صلى الله عليه وسلم) take to consolidate the Muslim community in Madina?
Ans: First of all, in order to establish an atmosphere of peace in Madina, he succeeded in drawing up the Constitution of Madina, also known as the Charter of Madina, between all the groups of Madina, through which a kind of understanding was developed among all the communities living in Madina. In later years, he unified the different Arab tribes under Islam, carried out social and religious reforms, and administrative developments that further consolidated the Islamic community in Madina.

Q.10: When did the Holy Prophet (صلى الله عليه وسلم) undertake his farewell pilgrimage to Makkah? What is its significance?
Ans: In the year 10 A.H., Prophet Muhammad (صلى الله عليه وسلم) undertook his farewell pilgrimage to Makkah This farewell pilgrimage is one of the most significant historical events for the Muslims, for it was the first and last pilgrimage made by Prophet Muhammad (صلى الله عليه وسلم), as well as an occasion when he taught Muslims how to perform Hajj.

Q.11: When and where did the Holy Prophet (صلى الله عليه وسلم) deliver his last (hajj) sermon?
Ans: Prophet Muhammad (صلى الله عليه وسلم) delivered his last (hajj) sermon in the Uranah valley of Mount Arafat, on 9th of Dhu al-Hijjah, 1 A.H. (6th March 632).

Q.12: What are the three points of the last (Hajj) sermon of the Holy Prophet (صلى الله عليه وسلم)?
Ans: The three main points of the last (hajj) sermon of Prophet Muhammad (صلى الله عليه وسلم) are:

1. Regard the life and property of every Muslim as a sacred trust.
2.  The superiority of men is not based on blood and wealth. In the sight of Allah everybody is equal. Only the goodness of a man makes him superior to others. The most righteous is the most honourable.
3. All the Muslims are brothers to each other.

Q.13: What did the Holy Prophet (صلى الله عليه وسلم) say about women in your last sermon?
Ans: He said, "It is true that you have certain rights with regards to your women, but they also have rights over you."

Q.14: What makes a man superior to others?
Ans: Only the goodness of a man makes him superior to others. No Arab is superior to a non-Arab. Nor is a white man in any way better than a black man. The claims to greatness founded on blood and wealth are false.

Q.15: What did the Holy Prophet (صلى الله عليه وسلم) say about the Muslims?
Ans: He said that a Muslim is another Muslim's brother. All the Muslims are brothers among themselves. It is due to the fact that all the men are the offspring of Adam. He also said that regard the life, honour and property of every Muslim as a sacred trust.

Q.16: What does the last sermon teach us?
Ans: The last sermon teaches us that:

• None shares the authority and power of God.
• The whole humanity is the offspring of Adam and the most righteous is the most honourable.
• Only the goodness of a man makes him superior to others.
• All the Muslims are brothers to each others.
• Life, honour and property of every Muslim is sacred trust.
• Hurt no one so that no one may hurt you.
• "Beware of Satan, for the safety of your religion. He has lost all hope that he will ever be able to lead you astray in big things, so beware of following him in small things."

Q.18: If the Muslims follow the messages given in the last sermon of the Holy Prophet (صلى الله عليه وسلم), what will be the result?
Ans: The messages conveyed in the last sermon are for all times. If the Muslims follow these messages, the result will be a fair and equitable society, in which there will be honesty and justice, and meritocracy will be the guiding principle.

Q.19: What must we do to be a good Muslim?
Ans: We should do good deeds to be a good Muslim.


(note: The answer of below question is taken  from old book)
Q.20: When, Where and On what three principles did the Holy Prophet (peace be upon him) found an Islamic Society?(KHI* Board-Science group 2005, 2009, 2011)
Ans. After migration, the Prophet Muhammad (peace be upon him) founded an Islamic Society in Medina based on the following three principles:

1. All power belongs to Allah.
2. Mohammad (peace be upon him) is the prophet of God.
3. All Muslims are brothers to one another.

English (Compulsory) For Class IX - Unit 1 - Ethics Character builder - MCQs and Fill In The Blanks

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The Last Sermon Of Holy Prophet (P.B.U.H)

MCQs and Fill In The Blanks

Multiple Choice Questions (M.C.Qs)

Read the text and tick (✓) OR circle the correct answer:
1. The text is about:
(a) the battles of Islam
(b) the family of Prophet Muhammad (صلى الله عليه وسلم)
(c) the migration and teachings of Prophet Muhammad (صلى الله عليه وسلم)
(d) the last pilgrimage. ✓

2. Which of the following message is mentioned in the Last Sermon, as given in the text?
(a) People should not hurt others.
(b) Both men and women have rights over each other
(c) Muslims are a part of one brotherhood.
(d) All of the above. ✓

3. How did the Quraish treat the Holy Prophet (صلى الله عليه وسلم)? They:
(a) favoured him
(b) opposed him, ✓
(c) loved him
(d) criticized him

4. When did the Holy Prophet (صلى الله عليه وسلم) migrated to Medina?
(a) 620 A.D.
(b) 621 A.D.
(c) 622 A.D. ✓
(d) 623 A.D.

5. When did the Holy Prophet (صلى الله عليه وسلم) settled in Madina, which of the following groups of people lived there?
(a) Muslims and Jews
(b) Muslims, pagans and Jews
(c) Muslims, pagans, hypocrites and Jews. ✓
(d) Muslims, hypocrites and Jews

6. Where did the Holy Prophet (صلى الله عليه وسلم) deliver his last sermon?
(a) Quba mosque
(b) Uranah valley. ✓ 
(c) Jaba-e-Rehmat
(d) Hudebia

7. When did the Holy Prophet (صلى الله عليه وسلم) perform his last Hajj?
(a) 6^th year of Hijra
(b) 8^th year of Hijra
(c) 10^th year of Hijra. ✓
(d) 12^th year of Hijra

8. When was the Holy Prophet (صلى الله عليه وسلم) was born?
(a) 560 A.D.
(b) 561 A.D.
(c) 570 A.D.
(d) 571 A.D. ✓

9. What did the Holy Prophet (صلى الله عليه وسلم) ask the Quraish?
(a) not to worship their false gods. ✓
(b) not to perform Hajj
(c) not to kill animals
(d) not to cheat

10. What was the old name of Madina?
(a) Madinatul-Nabi
(b) Yeman
(c) Yathrib. ✓
(d) Hudebia

11. At the time of arrival of the Holy Prophet (صلى الله عليه وسلم) in Madina, which community was huge in number?
(a) Muslims
(b) Hypocrites
(c) Pagans
(d) Jews. ✓

12. Prophet Muhammad (صلى الله عليه وسلم) was born in a respected family of:
(a) Banu Abbas
(b) Banu Umaiyads
(c) Quraish. ✓
(d) Banu Baker

13. Before the advent of Islam, the Quraish used to worship:
(a) the sun
(b) the moon
(c) stars. 
(d) idols. ✓

14. Prophet Muhammad (صلى الله عليه وسلم) was born in:
(a) 560 A.D.
(b) 571 A.D. ✓
(c) 572 A.D.
(d) 573 A.D.

15. Prophet Muhammad (صلى الله عليه وسلم) was born in:
(a) Makkah. ✓
(b) Madina
(c) Yathrib
(d) Quba

16. Quraish opposed the new faith so much that the Prophet (صلى الله عليه وسلم) had to ask the believers to migrate to:
(a) Makkah
(b) Yathrib. ✓
(c) Yeman
(d) Quba

17. The Prophet (صلى الله عليه وسلم) reached the outskirts of Yathrib on:
(a) 21^st June 622
(b) 25^th June 622
(c) 28^th June 622. ✓
(d) 29^th June 622

18. After eight days' journey, the Prophet (صلى الله عليه وسلم) stopped at a place called:
(a) Quba. ✓
(b) Madina
(c) Yeman
(d) Yathrib

19. The Prophet (صلى الله عليه وسلم) built a mosque at:
(a) Makkah
(b) Yeman
(c) Quba. ✓
(d) none of them

20. Prophet Muhammad (صلى الله عليه وسلم) entered Yathrib (Madina) on:
(a) 28th June 622
(b) 28th July 622
(c) 2nd June 622
(d) 2nd July 622. ✓

21. The event of the Prophet's (صلى الله عليه وسلم) migration to Madina is known as:
(a) miraj
(b) migration
(c) hijra. ✓
(d) A.D. 22.

22. This event marks the beginning of the Islamic calendar.
(a) Birth of the Prophet (صلى الله عليه وسلم )
(b) Miraj
(c) Death of the Prophet (صلى الله عليه وسلم)
(d) The Prophet's (صلى الله عليه وسلم) migration to Madina. ✓

23. After the migration of Prophet Muhammad (صلى الله عليه وسلم), Yathrib was soon renamed:
(a) Madinat un-Nabi. ✓
(b) un-Nabi
(c) the city
(d) All of them

24. "Madinat un-Nabi" means:
(a) the city
(b) the Prophet (صلى الله عليه وسلم)
(c) the center
(d) City of the Prophet (صلى الله عليه وسلم) .  ✓

25. In Madina, Prophet Muhammad (صلى الله عليه وسلم) succeeded in drawing up the Constitution of Madina, also known as:
(a) Chater of Madina. ✓
(b) the Agreement of Madina
(c) Sermon of Madina 
(d) All of them

26. Prophet Muhammad (صلى الله عليه وسلم) undertook his farewell pilgrimage to Makkah in the year:
(a) 7 A.H.
(b) 10 A.H. ✓
(c) 9 A.H.
(d) 11 A.H

27. All mankind is from Adam and Adam was created from:
(a) water
(b) fire
(c) dust. ✓
(d) stone

28. No Arab is superior to:
(a) another Arab
(b) a non-Arab. ✓
(c) a Turk
(d) an Egyptian

29. Man is made superior only on the basis of:
(a) worship
(b) wealth
(c) blood
(d) piety and good actions. ✓


30. In Allah's sight, the noblest of you is he who is the most:
(a) intelligent
(b) righteous
(c) God-fearing. ✓
(d) educated


31. Prophet Muhammad (صلى الله عليه وسلم) is the:
(a) first prophet
(b) last prophet. ✓
(c) primitive prophet
(d) None of them

English (Compulsory) For Class IX - Unit 1 - Ethics Character builder - Lesson with Urdu translation

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The Last Sermon Of Holy Prophet (صلى الله عليه وسلم)

Urdu Translation

رسول اللہ (صلى الله عليه وسلم) کا آخری خطبہ

Our Holy Prophet Muhammad (صلى الله عليه وسلم) is the last of the Prophets. Prophet Muhammad (صلى الله عليه وسلم) was born in 571 A.D. at Makkah Saudi Arabia, in a respected Quraish family. The Quraish used to worship idols and did not believe in one God. Prophet Muhammad (صلى الله عليه وسلم), asked the Quraish not to worship their false gods. He told them that he was the Prophet of Allah and asked them to accept Islam and to worship the One and only true God. Most of them refused to accept Islam. They thought that he was against their gods and their ancestors. They opposed this new faith so much that the Prophet (صلى الله عليه وسلم) had to ask the believers to migrate to Yathrib, a city 320 km (200 miles) north of Makkah.

But, with time, as many people started accepting his message and converting to Islam, the Quraish became more aggressive and started making attempts on his life. Hence, when Prophet Muhammad (صلى الله عليه وسلم) got positive signals from Yathrib, he also decided to emigrate there. After eight days' journey, he reached the outskirts of Yathrib, on 28^th June 622; but he did not enter the city directly. He stopped at a place called Quba', a place some miles from the main city, and built a mosque there.

On 2^nd July 622, Prophet Muhammad (صلى الله عليه وسلم) entered the city. This event is known as"Hijra"and marks the beginning of the Islamic calendar. Yathrib was soon renamed Madinat un-Nabi (literally "City of the Prophet"), but un-Nabi was soon dropped, and its name became "Madina", meaning "the city".

At the time of arrival of Prophet Muhammad (صلى الله عليه وسلم) in Madina, the city had four broad groups of people. There were the Muslims; including those who were from Madina and those who had emigrated from Makkah. Then, there were the hypocrites; that is those who embraced Islam in name only, but actually were against it. Additionally, there were the people from Aws and Khazraj, who were still pagans but were likely to accept Islam. Finally, there were the Jews, who were huge in number and formed an important community there.

In order to ensure that all these people lived peacefully with each other, Prophet Muhammad (صلى الله عليه وسلم) invited the leading personalities of all the communities to discuss this matter. He wanted the different groups to reach a formal agreement for harmony among the communities and for the security of the city of Madina. He succeeded in drawing up the Constitution of Madina, also known as the Charter of Madina, through which a kind of understanding was developed among all the communities living in Madina. It mentioned the rights and duties of the Muslims and the Jews of Madina, gave freedom of religion, and prohibited any alliance with the outside enemies. It also declared that any dispute would be referred to Prophet Muhammad (صلى الله عليه وسلم) for settlement. In later years, he unified the different Arab tribes under Islam, carried out social and religious reforms, and administrative developments that further consolidated the Islamic community in Madina.

In the year 10 A.H., Prophet Muhammad (صلى الله عليه وسلم) undertook his farewell pilgrimage to Makkah. This farewell pilgrimage is one of the most significant historical events for the Muslims, for it was the first and last pilgrimage made by Prophet Muhammad (صلى الله عليه وسلم), as well as an occasion when he taught Muslims how to perform the Hajj. Moreover, it was during this Hajj, that he delivered his last sermon in the Uranah valley of Mount Arafat, on the 9^th of Dhu al-Hijjah, 10 A.H. (6^th March 632). There were countless Muslims present with the Prophet (صلى الله عليه وسلم) during his last pilgrimage when he delivered his last Sermon.

Delivering his last sermon, Prophet Muhammad (صلى الله عليه وسلم) first of all praised and thanked Allah, and then said, "0 people, lend me an attentive ear, for I know not whether, after this year, I shall ever be amongst you again. Therefore, listen to what I am saying to you very carefully and take these words to those who could not be present here today."
Then, amongst other things, he gave the following messages:
"0 People! regard the life and property of every Muslim as a sacred trust. Return the goods entrusted to you to their rightful owners. Hurt no one so that no one may hurt you."
"Beware of Satan, for the safety of your religion. He has lost all hope that he will ever be able to lead you astray in big things, so beware of following him in small things."
"0 People, it is true that you have certain rights with regard to your women, but they also have rights over you."

"All mankind is from Adam and Adam was created from dust. The noblest of you in Allah's sight is the most God-fearing. An Arab has no superiority over a non-Arab, nor does a non-Arab have any superiority over an Arab; a white has no superiority over a black, nor does a black have any superiority over a white, except by piety and good action. I, therefore, crush under my feet all the false claims to greatness and superiority founded on blood or wealth."

"Every Muslim is a brother to every Muslim and that the Muslims constitute one brotherhood. Nothing shall be legitimate to a Muslim which belongs to a fellow Muslim unless it was given freely and willingly."
The Holy Prophet completed His last sermon by saying, "Be my witness, 0 God, that I have conveyed your message to your people."
The messages conveyed in this sermon are for all times. If the Muslims follow these messages, the result will be a fair and equitable society, in which there will be honesty and justice, and meritocracy will be the guiding principle.

English (Compulsory) For Class IX - Unit 1 - Ethics Character builder - Words / Meanings and Summary

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The Last Sermon Of Holy Prophet
(Peace Be Upon Him)

Words / Meanings

S.NO.	Words	Meanings
1.	Aggressive	Likely to attack, Belligerent
2.	Alliance	A kind of working relationship, Union
3.	Analogies	Similar families / condition between two things.
4.	Ancestors	Fore fathers or Family members who were before the grandparents
5.	Anecdotes	Short, amusing, real stories.
6.	Astray	Away from the correct path or direction
7.	Attempts on his life	An act of trying to kill him
8.	Belongs	Relates
9.	Beware	Be careful, Be cautious and alert
10.	Complaining	Saying that one is feeling pain or is not happy or not satisfied with something
11.	Consolidate	Make secure or strong
12.	Constitute	Form or compose
13.	Contitution	The basic laws of nation
14.	Conveyed	To communicate or to carry or to pass on information.
15.	Embraced	Hold closely in one's arms
16.	Emigrate	Leave one's own country in order to settle permanently in another.
17.	Entrust	Endow
18.	Equitable	Fair and justice
19.	Event	Incident, Public or social occasion.
20.	Faith	Belief
21.	Farewell	Marking someone's departure.
22.	Glass	A container used for drinking something.
23.	Greatness	Magnitude
24.	Guiding principle	Rule that set the direction one take
25.	Harmony	Compatibility in opinion and action, Understanding and accepting each others' thoughts and feelings.
26.	Honest	Truthful
27.	Hypocrites	People who pretend to be what they are not, Phoney
28.	Idols	False Gods, Image for worship
29.	Legitimate	Lawful, According to the rules and laws.
30.	Manner	The way in which something is done.
31.	Meritocracy	Giving awards and positions to people according to their capability and performance, A society governed by people selected according to merit.
32.	Migrate	leave one's own country in order to settle permanently in another, relocate, resettle.
33.	Occasion	Event
34.	Oppose	Resist
35.	Outskirts	The outer part of a city.
36.	Pagans	People who do not believe in any of the main religions of the world, Heathen, Infidel.
37.	Perform	do, carry out, accomplish.
38.	Piety	Strictly following the teachings of one's religion, The quality of being religious.
39.	Pilgrimage	Religious journey,
40.	Principle	A rule for behaving in a certain way, basis, essence
41.	Prohibited	Did not allow doing something, Banned.
42.	Prophet	God's messenger
43.	Reforms	make changes in (something, especially an institution or practice) in order to improve it, make better
44.	Sacred	Holy
45.	Sermon	Leccture (Religious)
46.	Sight	in vision
47.	Significance	Importance
48.	Society	The community.
49.	Superiority	the state of being superior, To be higher in rank or position
50.	Tribe	Clan
51.	True	Correct
52.	Unified	Make or become united, Linked people together.
53.	Woods	An area of land, smaller than a forest, covered with growing trees.
54.	Worships	Reverence.

Summary

Prophet Muhammad (P.B.U.H) was the last Prophet of God. He was born 571 A.D. in Makkah. He belonged to the noble family of Quraish. When he (P.B.U.H) began to preach Islam, and told Quaraish that only Allah is the worthy of worship. The people of Makkah turned against him and became his fierce enemy, as they thought that Islam was against their gods and ancestors.
Due to their opposition the holy Prophet (peace be upon him) asked his(peace be upon him) followers to migrate to Yathrib (Medina). In June 622 A.D. first he (P.B.U.H) reached at Quba and built a mosque there, then in July 622 A.D. they emigrated to Madinah. This event is called Hijra and marks the beginning of the Islamic calendar.
At the time of arrival of Prophet Muhammad (P.B.U.H) in Madinah, there were living four broad group: Muslims, hypocrites, pagans and jews together. He succeeded in drawing up the constitution of Madina, known as Charter of Madina, through which a kind of understanding was developed among all the communities living in Madina. The Charter of Madina and the Prophet's (P.B.U.H) reforms consolidated the Islamic community in Madina.
In the 10^th Hijri, he (P.B.U.H) performed his first and last Hajj with his followers. He (P.B.U.H) gave his last hajj sermon on in the Uranah Valley of Mount Arafat. The main points of his sermon are as follows:
He(P.B.U.H) first of all praised and thanked Allah than asked those people who were present there, to convey his words to others also. He told that regard the life and property of every Muslim as a sacred trust. Hurt no one. Beware of Satan, for the safety of our religion. Both men and women have rights over each other. The superiority of man is not based on blood and wealth. In the sight of Allah everybody is equal, only the piety and goodness of a man makes him superior to others. All the Muslims are brothers. The most righteous is the most honourable. The Holy Prophet (P.B.U.H) completed his last sermon by asked God to be witness. The message conveyed in this sermon are for all times.

English (Compulsory) For Class IX - Glossary or Words / Meanings

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GLOSSARY
Words / Meanings From All Chapters

A

S.NO.	Words	Meanings
1.	Abundance	A large quantity.
2.	Access	Be within reach for use.
3.	Accomplishments	Achievements.
4.	Acumen	The ability to understand things quickly and clearly.
5.	Aggressive	Likely to attack.
6.	Air	The mixture of gases that all living things breathe.
7.	Airs	Showing-off manner.
8.	Alliance	A kind of working relationship.
9.	Analogies	Similar families / condition between two things.
10.	Ancestors	Family members who were before the grandparents.
11.	Ancestral roots	Place where forefathers lived.
12.	Anecdotes	Short, amusing, real stories.
13.	Antibodies	Substances in the blood that fight against diseases.
14.	Arm	Shoulder to the hand part of the human body.
15.	Arms	Weapons, e.g., guns or explosives.
16.	Arrogant	Behaving in a proud manner.
17.	Aspects	Particular parts or sides.
18.	Aspirations	Strong desires.
19.	Astray	Away from the correct path or direction.
20.	Attain	Succeed in getting.
21.	Awhile	For a short time.

B

S.NO.	Words	Meanings
22.	Backdrop	Background.
23.	Beetle nut	A hard small nut that people in some parts of the world chew.
24.	Beware	Be careful
25.	Bitter	Feeling great dislike or anger.
26.	Blessed	Fortunate.
27.	Blithe	Without cares and worries.
28.	Boast	Source of pride.
29.	Bold	Confident and brave.
30.	Borne	Put up with.
31.	Break of day	Dawn.
32.	Burden	Main part.

C

S.NO.	Words	Meanings
33.	Calligraphy	Artistic handwriting.
34.	Capture	Get control over something.
35.	Character	Qualities that people show in their behaviour.
36.	Characters	Persons in a novel, play, etc.
37.	Chills	Feeling of coldness
38.	Clarification	Make something clear and easy to understand.
39.	Clot	A lump formed in the blood, which stops or disturbs the flow of blood.
40.	Collapse	To sit or lie down and relax, especially after working hard, etc.
41.	Compile	To collect information together.
42.	Commences	Begins.
43.	Commuting	Travelling from one place to another.
44.	Complaining	Saying that one is feeling pain or is not happy or satisfied with something.
45.	Compromised	Adversely affected.
46.	Consolidated	Made secure or strong.
47.	Constipation	Not able to discharge solid waste from the body.
48.	Consult	Go to someone for advice.
49.	Contact	Touch in some way.
50.	Contagious	A disease that can spread by touch.
51.	Contribution	Time, money, effort or skill given for a cause.
52.	Count on	Depend on/ consider.
53.	Credit	Sell something for which the buyer pays later.
54.	Culminating	Resulting in achieving what is wanted.
55.	Cunning	Clever at cheating people.
56.	Custom	A traditional and usually acceptable way of behaving or doing things.
57.	Customs	The government department that collects taxes on goods brought in from other countries.

D

S.NO.	Words	Meanings
58.	Departed	Left.
59.	Desperately	Very much.
60.	Destitute	Very poor/ not having any money.
61.	Determined	Not changing a decision once made.
62.	Devastation	Great destruction or damage
63.	Devices	Things used for a particular purpose
64.	Devotees	People who have faith in a particular religion or religious person.
65.	Discover	Find out.
66.	Discrimination	Different treatment for different people.
67.	Disorientation	Loss of sense of direction.
68.	Display	To put up something in a place where people can see it easily.
69.	Distanced	Taken away.
70.	Distinction	Difference.
71.	Doffed	Took off his hat in respect.
72.	Dwelt	Lived in or at a place.
73.	Dynamic	Having a lot of energy.
74.	Dysfunction	Problem in the working of some part of the body.

E

S.NO.	Words	Meanings
75.	Elegance	Attractiveness.
76.	Elegant	Attractive.
77.	Embodiment	Solid form or shape.
78.	Enthusiasm	A strong feeling of excitement.
79.	Envisioned	Imagined as a future possibility.
80.	Envy	The feeling of wishing to have what somebody else has or to be like somebody else.
81.	Equitable	Fair and just.
82.	Evaded	Did not come within reach.
83.	Expel	Take out.

F

S.NO.	Words	Meanings
84.	Fatal	Causing or ending in death,
85.	Force	The strength or power of something.
86.	Forces	An organized body of armed and specially trained people.
87.	Foremost	Leading.
88.	Frequently	Very often.

G

S.NO.	Words	Meanings
89.	Glanced	Gave a quick look.
90.	Glass	A container used for drinking something.
91.	Glasses	A pair of lenses in a frame that rests on the nose and ears.
92.	Gossips	Stories about other people's lives.
93.	Grandeur	Great and impressive appearance.
94.	Grateful	Feeling thankful for something.
95.	Grief	Deep sadness.
96.	Guiding principles	Rules that set the direction one takes.

H

S.NO.	Words	Meanings
97.	Hale	Strong and healthy.
98.	Harmony	Understanding and accepting each others' thoughts and feelings.
99.	Havoc	Great damage or destruction.
100.	Homage	Something said or done to show great respect.
101.	Hospitality	Treating guests in a generous and welcoming manner.
102.	Hosted	Organised an event.
103.	Hypocrites	People who pretend to be what they are not.

I

S.NO.	Words	Meanings
104.	Identical	The same.
105.	Immune	Cannot be harmed by a disease because the body has developed the ability to fight it.
106.	Impartiality	Not favouring any one person.
107.	Implementing	Putting into effect.
108.	Impressive	worth admiring.
109.	Inflammation	A condition in which a part of the body is red, swollen and sore.
110.	Insignificant	Unimportant/ having no value
111.	Inspired	To develop a feeling or aim in someone for doing something.
112.	Intense	Very great or severe.
113.	Intonation	Use and fall of the voice in speaking.
114.	Irrigation	Supplying water for the growth of crops.

L

S.NO.	Words	Meanings
115.	Lark	A small brown bird.
116.	Legitimate	According to the rules and laws.
117.	Longing	Deep felt wish/ desire.

M

S.NO.	Words	Meanings
118.	Manner	The way in which something is done.
119.	Manners	Polite social behaviour.
120.	Mealy	Shabby.
121.	Meritocracy	Giving awards and positions to people according to their capability and performance.
122.	Migrate	To move from one place to go or live in another place.
123.	Miller	A person who owns or works a mill for grinding corn.
124.	Moth	A flying insect that is attracted to light.
125.	Mystic	A person who has spiritual power due to nearness to God.

N

S.NO.	Words	Meanings
126.	Nausea	A feeling of wanting to be sick.
127.	Navigation	Directing a ship or other vehicle for reaching a place.

O

S.NO.	Words	Meanings
128.	Omnipotence	Having total power.
129.	Opinions	Thoughts and ideas.
130.	Oral	Traditions information passed by word of mouth from one generation to the next.

P

S.NO.	Words	Meanings
131.	Pagans	People who do not believe in any of the main religions of the world.
132.	Parasite	An animal or plant that lives on or in another and gets its food from it.
133.	Philanthropist	A person who supports good causes, especially by giving money.
134.	Piety	Strictly following the teachings of one's religion.
135.	Pluralistic	Different groups of people living together in peace.
136.	Polarization	Separation into two opposite groups.
137.	Pondered	Think carefully for a long time before deciding
138.	Pose	Pretend.
139.	Predicate	A part of the statement that says something about the subject.
140.	Preoccupied	Not paying attention because thinking or worrying about something else.
141.	Prevailed	Widespread.
142.	Principle	A rule for behaving in a certain way.
143.	Prohibited	Did not allow doing something.
144.	Pronounced	Very noticeable
145.	Proponent	A person who supports a cause.

Q

S.NO.	Words	Meanings
146.	Quest	Search.
147.	Quoth	Said.

R

S.NO.	Words	Meanings
148.	Realize	To make one's dreams, ideas, plans, etc. happen
149.	Recall	Remember
150.	Reciprocal	Act the language according to the situation.
151.	Recognition	Officially recognizing somebody's ability or achievements, often by giving an award.
152.	Rehearse	To practise privately what one is going to say or do.
153.	Release	Let go
154.	Relevant	Relating to or bearing upon the matter in hand.
155.	Reluctantly	Unwilling, therefore slow to act, agree, etc.
156.	Renowned	Famous.
157.	Replaced	Taken the place of.
158.	Respiratory	Breathing related.
159.	Restless	Unable to stay still or be happy where one is.
160.	Retain	Hold back.
161.	Reverence	A feeling of great respect and admiration.

S

S.NO.	Words	Meanings
162.	Saliva	Liquid produced in the mouth that helps one swallow and digest food.
163.	Self-respect	Having a sense of pride for being/ having something.
164.	Self-sufficient	Have enough to meet one's needs.
165.	Shabby	In poor condition through much use or being badly cared for.
166.	Shrewd	Clever.
167.	Siblings	Brothers and sisters.
168.	Sighed	Took a long deep breath.
169.	Sight	A person or thing that looks bad or untidy.
170.	Sights	The places of interest, especially in a town or city, that are often visited by tourists.
171.	Simultaneously	At the same time.
172.	Sparkling	Shining
173.	Spectacle	The happening of something that is not accepted as normal.
174.	Spectacles	Glasses worn to improve a person's sight.
175.	Splendour	Grand and impressive beauty.
176.	Stagnant	Standing in one place, not flowing or moving.
177.	Steadfastness	Firmly staying on one path.
178.	Straightaway	Immediately.
179.	Structures	Things made of several parts.
180.	Sufferings	People having physical or mental pain.
181.	Superiority	To be higher in rank or position.
182.	Supplication	Humble request/prayer.
183.	Supportive	Giving help and sympathy.
184.	Surplus	More than the amount needed.

T

S.NO.	Words	Meanings
185.	Tamed	Made easy to control.
186.	Tender	Kind, gentle and loving.
187.	Thee	You.
188.	Thine	Your.
189.	Thou'dst	You would.
190.	Thou'rt	You are.
191.	Tireless	Working without showing any signs of being tired.
192.	Transform	Change into something else.
193.	Transfusion	Putting of one person's blood into another person's body.
194.	Transmitted	To pass something from one person, place or thing to another.

U

S.NO.	Words	Meanings
195.	Undesired	Unacceptable/ unwelcome.
196.	Unified	Linked people together.
197.	Universal	Applicable to or done by most people in the world.
198.	Unparalleled	So great that there is nothing else like it.
199.	Utensils	Pots, pans, etc. used for cooking or serving food.

V

S.NO.	Words	Meanings
200.	Versatile	Moving easily from one subject, skill, or occupation to another.
201.	Victimization	Unfair suffering.
202.	Voyages	Long journeys by sea.

W

S.NO.	Words	Meanings
203.	Weathered	Brown, rough and lined or damaged skin because one has spent a lot of time outside in the sun and wind.
204.	Wood	Material made from the trunk and branches of a tree.
205.	Woods	An area of land, smaller than a forest, covered with growing trees.

English (Compulsory) For Class IX - Unit 2 - Role Model - Text Book Exercise Unit 2.1 (Exercise 1 - 7)

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Shah Abdul Latif Bhitai

TEXT BOOK EXERCISE:

UNIT 2.1 READING COMPREHENSION

While Reading
Exercise 1:
a) How many aspects of Shah Abdul Latif's life have been covered in the text?
Ans: There are seven aspects of Shah Abdul Latif's life have been covered in the text.

b) List all these aspects in your notebook as shown below.
Ans: Following are the aspects of Shah Abdul Latif's life:

1. The first aspect is about his Background and Family.
2. The second aspect is about his name Bhitai.
3. The third aspect is about his early life and education.
4. The fourth aspect is about his youth.
5. The fifth aspect is about his spiritual growth.
6. The sixth aspect is about his death and remembrance.
7. The seventh aspect is about Shah Latif's poetry.

Vocabulary
Exercise 2:
The words given in bold below have been taken from the text. Look up these words in the text and underline them.
Next, do the following exercise. Underline the correct answers from the choices provided. The first one has been done as an example.
1. Those who have an abundance of wealth have
(a) little wealth
(b) a lot of wealth
(c) some wealth

2. My family's ancestral roots are in Sindh, means my parents, grandparents and great grandparents have lived in Sindh since
(a) my grandparents got married
(b) my birth
(c) many generations

3. The new academic year commences in our school in April.
(a) ends
(b) progresses
(c) begins

4. The devotees of some saints walk to shrines barefoot.
(a) children
(b) followers
(c) caretakers

5. Many people go to a mystic to ask for the fulfillment of their wishes.
(a) person who lives alone
(b) new person
(c) person with spiritual power

6. The sailors of Sindh used to travel to far off lands as they had good navigation skills.
(a) ship directing
(b) engineering
(c) swimming

7. For centuries, the main medium for transfer of information was oral traditions.
(a) horses
(b) passing of information by word of mouth
(c) messages

8. My brother is a restless person, always looking for new things to do.
(a) genius
(b) different
(c) change seeking

9. Truly great persons deserve reverence as they play a positive role in our lives.
(a) richness and wealth
(b) leadership positions
(c) respect and admiration

10. Islam's message of peace is universal, as without it there can be no happiness.
(a) good
(b) applicable to all the people in the world
(c) acceptable

Exercise 3:
Work in pairs and complete the sentences below with a word written in bold in Exercise 2.
You can use one word only once. Write the complete sentences in your notebook.
1. The devotees of Shah Bhitai celebrate his Urs every year.
2. My mother and I decided to go to a mystics to ask him to pray for my father's health.
3. It is a universal fact that no living thing can survive without oxygen.
4. Much of what we know about our culture has been passed on to us through oral traditions.
5. We may have different ancestral roots but we are all the off springs of Adam.
6. Fasting commences on the first day of Ramadan.
7. Pakistan has everything in abundance but we need strong policies to make good use of everything that we have.
8. Nelson Mandela won his people's reverence for his long struggle for the rights of people in South Asia.
9. The art of restless requires hard work and one needs to practise a lot to write beautifully.
10. The Pakistan Navy has very good navigation skills.


Exercise 4:
The reading text has seven aspects that relate to Shah Latif.
The following sentences state one key point covered under each aspect. However, these sentences are in a jumbled up order. Read the text and write the aspect number in the blanks provided. The last one has been done for you as an example.
a) He found pleasure in praying, thinking and devotion. 5
b) He was married for a short period of time only. 4
c) Shah Latif's forefather migrated to Sindh from Afghanistan. 1
d) A shrine was built over his grave sometime after his death. 6
e) His poetry is mainly about Sindh but off places are also mentioned. 7
f) He loved studying and had a command over other languages. 3
g) He is called Bhitai because he spent a good past of his life on a mound. 2


Exercise 5:
Read the text and find the following information. Write down these things in your notebook. After you have completed, discuss your answers with your partner.
1. Two things done at the time of `Urs', as mentioned in the text.
Ans: Two things done at the time of `Urs' are:

1. Thousands of people gather and listen to the saint's songs sung on the Tambooro'.
2. Many learned men read papers that tell about Latif's life and his poetry.

2. Two possible reasons why his ancestors migrated to Sindh.
Ans: Reason due to which Shah Latif's ancestors migrated to Sindh.

1. The Shah's father, Syed Habib Shah, migrated from Matyaru, his ancestral home in Afghanistan, to Bhainpur in Sindh, in order to gain spiritual contact with Bilawal, a local pious man.
2. His ancestors migrated to Sindh from Hirai Sindh was then a centre of Muslim culture and Shah Lath's ancestors liked it so much that they decided to make it their home.

3. Two other languages that he knew quite well.
Ans: Two other languages that Shah Latif knew quite well:

1. Arabic
2. Persian

4. Two main religious sources that he had knowledge about.
Ans: Two main religious sources that Shah Latif had knowledge about

1. Holy Quran
2. Hadith

5. Two poets whose works were a part of his collection.
Ans: Two poets whose works were a part of Shah Latif's collection.

1. Moulana Jalaluddin Rumi
2. Shah Karim

6. Two skills for which he is known.
Ans: Two skills for which Shah Latif is known

1. Poet
2. Sufi Saint

7. Two places in Afghanistan mentioned in his poetry.
Ans: Two places in Afghanistan mentioned in his poetry.

1. Kabul
2. Kandahar

8. Two places in India mentioned in his poetry.
Ans: Two places in India mentioned in his poetry are:

1. Delhi
2. Deccan

9. Two languages mentioned in which the Risalo' has been translated.
Ans: Two languages in which the Risalo' has been translated.

1. English
2. Urdu

Exercise 6:
a) How was information about Shah Latif's early life collected. Why was it collected in this manner?
Ans: Information about the life of Bhitai has mostly been collected from oral traditions. Because at that time the information of history or the past people were passed by words of mouth from one generation to next. So a renowned Pakistani scholar, educationist, and writer of plays, dramas and stories, Mirza Kalich Beg, is said to have collected details about the early life of Shah Bhitai from some of the old people living at that time. These people had heard these facts from their fathers and grandfathers, some of whom had seen Shah Latif in person and had even spoken to him.

b) Why is Shah Latif called the 'Saint of Bhit'?
Ans: In 1742, Shah Latif left his home and went to live on a mound at some distance from his village, A mound of sand is called 'Bhit' in Sindh, Due to the fact that he lived on this mound for the rest of his life, Shah Latif came to be known as 'Saint of Bhit.' To this day, he is famous all over the country as Shah Abdul Lath Bhitai or Shah Latif of the Mound.

c) Why did Shah Latif not marry again after his wife died?
Ans: In 1713 the Sufi poet married with Bibi Saidha Begum. His wife died at an early age, before she could have any children. However, Shah never married again. Because after the death of his wife, his heart turned more and more towards religion and devotion and he felt restless; and he found it difficult to live a normal domestic life.

d) Why did people become Shah Latif's followers?
Ans: Latif's love of God grew more and more, to the extent that he found pleasure only in devotion. As a result, he spent most of his time in prayers and deep thinking. His spiritual power grew stronger with prayers and devotion so much, so that people began to be attracted towards him. Anyone who came to see him was strongly impressed by his gentle ways and became his devotees. In this way his followers increased day by day.

e) What does Shah Latif's poetry and work tell us about his knowledge and skills?
Ans: Shah Abdul Latif was a sensitive, gentle and kind soul. He was a Sufi in the true sense of the word. Besides its simplicity, one great quality of Latif's poetry is its moving music. The word 'latif' literally means fine, delicate, tender, elegant, and light. This meaning is truly reflected in both his poetry and his personality. His poetic nature loved the calm atomsphere and are spiritual and mystic. Moreover, he was a poet of the people, so he wrote in the language of the common man.

f) Name the places in the text mentioned in Shah Latif's poetry. Why do you think these places have been mentioned by him?
Ans: In his poems he writes mainly about Sindh and its neighbouring regions. However, he also mentions distant cities, such as Istanbul (Turkey) and Samarqand(Uzbekistan), China, Rome, Kabul and Kandahar (Afghanistan), Delhi and Deccan (India). He mentioned these places because he talks about Sindhi sailors (Samundi), their navigation techniques, and their voyages as far as the Malabar coast, Sri Lanka and the island of Java and all above places.

g) Why is Shah Latif's key message in his verses acceptable to everyone?
Ans: His spiritual and mystic poetry carries a message of love, which makes it universal and acceptable to the entire human race. Shah Abdul Latif Bhitai is, and always will be, remembered for his great poetry with love and reverence.

h) Can we put his message into practice in today's world. If 'Yes' how, if `No' why not?
Ans: Yes, we put Latif's message into practice in today's world because his message is the message of love. He believed in brotherhood and equality of men and in pleasing God by good deeds. This according to him is the goal of life.

Exercise 7:
Work in groups of six and prepare questions for conducting an interview of scholars who have studied Shah Abdul Latif Bhitai, his life and his poetry.
Next, prepare a role play in which one member of the group becomes an anchor person while the remaining members become scholars in a TV talk show.

Mathematics For Class IX Science - Unit 01 - SETS - Exercise 1.2

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Unit 01: SETS
EXERCISE 1.2

Q.1: Given that the sets A = {f, a, c, e} and B = {e, g, d, f } are subsets of the Universal Set U = {a, b, c, d, e, f, g}, list the elements of:
(1) A' (2) B' (3) A∩B (4) (AUB)' (5) A∩B' (6) A'∩B' (7) UUØ (8) U∩Ø

(1) A'
Solution:
A' = U - A
= {a,b,c,d,e,f,g} - {f,a,c,e} = {b,d,g}
∴ A' = {b,d,g} Ans.

(2) B'
Solution: B' = U - B'
= {a,b,c,d,e,f} - {e,g,d,f} = {a,b,c}
∴ B' = {a,b,c} Ans.

(3) A∩B
Solution:
A∩B = {f,a,c,e} ∩ {e,g,d,f}
∴ A∩B = {e,f} Ans.

(4) (AUB)'
Solution:
AUB = {f,a,c,e} U {e,g,d,f}
AUB = {a,c,d,e,f,g}
(AUB)' = U - (AUB) = {a,b,c,d,e,f,g} - {a,c,d,e,f,g}
∴ (AUB)' = {b} Ans.

(5) A∩B'
Solution:
B' = U - B = {a,b,c,d,e,f,g} - {e,g.d,f}
B' = {a,b,c}
A∩B' = {f,a,c,e} ∩ {a,b,c} ∴ A∩B' = {a,c } Ans.

(6) A'∩B'
Solution:
A' = U - A = { a,b,c,d,e,f,g) - {f,a,c,e}
A' {b,d,g}
B' = U - B = {a,b,c,d,e,f,g} - {e,g,d,f}
B' {a,b,c}
A'∩B' = {b, d, g} ∩ {a,b,c}
∴ A'∩B' = {b} Ans.

(7) UUØ
Solution:
UUØ = { a,b,c,d,e,f,g} U { } = { a,b,c,d,e,f,g }
∴ UUØ = { a,b,c,d,e,f,g } = U Ans.

(8) U∩Ø
Solution:
U∩Ø = {a,b,c,d,e,f,g} ∩ { }
∴ U∩Ø = { } Ans.

Q.2: Given the sets:
A = (x | x is positive even integer less than 10} and B = {x | x is positive odd integer less than 10} are subsets of the universal set U = {x | x is a positive integer less than 10} list the elements of:
(9) AUB' (10) A'∩B (11) A'∩B' (12) AΔB (13) A - B' (14) A'ΔB (15) (A'∩B)'

Solution:
In tabular form
A = {2,4,6,8}
B = {1,3,5,7,9}
U = {1,2,3,4,5,6,7,8,9}

(9) AUB'
Solution: A = {2,4,6,8}
B = {1,3,5,7,9}
U = {1,2,3,4,5,6,7,8,9}
B' = U-B = { 1,2,3,4,5,6,7,8,9} - (1,3,5,7,9}
B' = {2,4,6,8}
Now
AUB' =. {2.4,6,8} U {2,4,6,8}
∴ AUB' = {2,4,6,8} Ans.

(10) A'∩B
Solution:
A' = U - A = {1,2,3,4,5,6,7,8,9} - {2,4,6,8}
A' = (1,3,5,7,9)
A'∩B = (1,3,5,7,9) ∩ {1,3,5,7.9}
∴ A'∩B = { } Ans.

(11) A'∩B'
Solution:
A' = U - A = {1,2,3,4,5,6,7,8,9} - {2,4,6,8}
A' = {1,3,5,7,9}
B' = U - B = {1,2,3,4,5,6,7,8,9} - (1,3,5,7,9)
B' = (2,4,6,8)
A'∩B' = {1,3,5,7,9} ∩ {2,4,6.8}
∴ A'∩B' = { } Ans.

(12) AΔB
Solution:
As AΔB = AUB - A∩B
AUB = {2,4,6,8} U {1,3,5,7,9}
AUB = {1,2,3,4,5,6,7,8,9}
A∩B = {2,4,6,8} ∩ {1,3,5,7,9}
A∩B = { }
Now
AΔB = AUB - A∩B
AΔB = {1,2,3,4,5,6,7,8,9} - { }
∴ AΔB = {1,2,3,4,5,6,7,8,9} Ans.

(13) A - B'
Solution:
B' = U - B = { 1,2,3,4,5,6,7,8,9} - {1,3,5,7,9}
B' = {2,4,6,8}
A - B' = {2,4,6,8) - {2,4,6,8}
∴ A - B' = { } Ans.

(14) A'ΔB
Solution:
A' = U - A = {1,2,3,4,5,6,7,8,9} - {2,4,6,8}
A' = {1,3,5,7,9}
As A'ΔB = A'UB - A'∩B
A'UB = {1,3,5,7,9} U {1,3,5,7,9}
A'UB = {1,3,5,7,9}
A'∩B = {1,3,5,7,9} ∩ {1,3,5,7,9}
A'∩B = {1,3,5,7,9}
Now
A'ΔB = A'UB - A'∩B
A'ΔB = (1,3,5,7,9) - {1,3,5,7,9}
∴ A'ΔB = { }

(15) (A'∩B)'
Solution:
A' = U - A = { 1,2,3,4,5,6,7,8,9} - {2,4,6,8}
A' = {1,3,5,7,9}
As (A'∩B)' = U - (A'∩B)
A'∩B = { 1,3,5,7,9} ∩ {1,3,5,7,9}
A'∩B = {1,3,5,7,9}
Now
(A'∩B)' = U - (A'∩B)= {1,2,3,4,5,6,7,8,9} - {1,3,5,7,9}
∴ (A'∩B)' = {2,4,6,8} Ans.

(16) Draw the Venn diagrams for the sets in Questions # 9, 10, 11, 12, 13, 14 and 15.

(9) Venn diagrams AUB'

(10) Venn diagrams A'∩B

(11) Venn diagrams A'∩B'

(12) Venn diagrams AΔB

(13) Venn diagrams A - B'

(14) Venn diagrams A'ΔB

(15) Venn diagrams (A'∩B)'

If A = {1, 2, 3, 4} and B = {2, 4, 6, 8}, show that:
(17) AΔB = (AUB) - (A∩B)
(18) AΔB = (A - B) U (B - A)
(19) A - B = A - (A∩B)

(17) AΔB = (AUB) - (A∩B)
Solution:
Taking L.H.S:
AΔB = (1,2,3,4) Δ (2,4,6,8)
(By selecting uncommon members among both sets)
We get AΔB = {1,3,6,8} ....... (1)
Taking R.H.S:
AUB = (1,2,3,4) U (2,4,6,8)
AUB = (1,2,3,4,6,8)
A∩B = {1,2,3;4} ∩ {2,4,6,8)
A∩B = (2,4)
AUB - A∩B = (1,2,3,4,6,8) - {2,4}
We get AUB - A∩B = (1,3,6,8) ....... (2)
By (1) and (2)

AΔB = AUB - A∩B Hence Proved

(18) AΔB = (A - B) U (B - A)
Solution:
Taking L.H.S:
AΔB = {1,2,3,4} Δ {2,4,6,8}
AΔB = (1,3,6.8) ....... (1)
Taking R.H.S:
(A - B) U (B - A)
A - B = (1,2,3,4) - (2,4,6,8)
A - B = (1,3)
B - A = (2,4,6,8) - (1,2,3,4)
B - A = (6,8}
(A - B) U (B - A) = (1,3) - (6,8) = (1,3,6,8) ......... (2)
By (1) and (2)

AΔB = (A - B) U (B - A) Hence Proved. 

(19) A - B = A - (A∩B)
Solution:
Taking L.H.S:
A - B = (1,2,3,4) - (2,4,6,8)
A - B = (1,3) ....... (1)
Taking R.H.S:
A - (A∩B) = {1,2,3,4} - {(2,4,6,8) ∩ (2,4)}
A - (A∩B) = (1,2,3,4) - {2,4}
A - (A∩B) = {1,3} ....... (2)
By (1) and (2)

A - B = A - (A∩B Hence Proved.

Example No.1:
Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 3, 5, 7} and B = {3, 4, 5, 6} Verify De Morgan's Laws.

Solution:
According to De Morgan's Laws
1. (AUB)' = A'∩B'
2. A'UB' = (A∩B)'

1. (AUB)' = A'∩B'
Taking L.H.S:
(AUB)' = U - AUB
AUB = {1, 3, 5, 7} U {3, 4, 5, 6}
AUB = {1,3,4,5,6,7}
U - AUB = {1, 2, 3, 4, 5, 6, 7} - {1,3,4,5,6,7}
∴ (AUB)' = {2} ..... (1)
Taking R.H.S:
A'∩B'
A' = U - A
A' = {1, 2, 3, 4, 5, 6, 7} - {1, 3, 5, 7}
A' = {2,4,6}
B' = U - B
B' = {1, 2, 3, 4, 5, 6, 7} - {3, 4, 5, 6}
B' = {1,2,7}
A'∩B' = {2,4,6} ∩ {1.2.7}
∴ A'∩B' = {2} .... (2)
By (1) and (2)

(AUB)' = A'∩B'

Hence De Morgan's Laws has proved

2. A'UB' = (A∩B)'
Taking L.H.S
A'UB'
A' = U - A
A' = {1, 2, 3, 4, 5, 6, 7} - {1, 3, 5, 7}
A' = {2,4,6}
B' = U - B
B' = {1, 2, 3, 4, 5, 6, 7} - {3, 4, 5, 6}
B' = {1,2,7}
A'UB' = {2,4,6} U {1,2,7}
∴ A'UB' = {1,2,4,6,7} ....... (1)
Taking R.H.S:
(A∩B)'
A∩B = {1, 3, 5, 7} ∩ {3, 4, 5, 6}
A∩B = {3,5}
(A∩B)' = U - (A∩B)
U - (A∩B) = {1, 2, 3, 4, 5, 6, 7} - {3.5}
∴ (A∩B)' = {1,2,4,6,7} ...... (2)
By (1) and (2)

A'UB' = (A∩B)'

Hence De Morgan's Law has proved

(20) If U = {1, 2, 3, . 20}, A = {1, 2, 4, 8, 10, 16, 20} and B = {2, 6, 8, 10, 14, 18}, verify De Morgan's Laws.

Solution:
According to De Morgan's Laws
1. (AUB)' = A'∩B'
2. A'UB' = (A∩B)'

1. (AUB)' = A'∩B'
Solution:
For L.H.S:
(AUB)' = U - AUB
AUB = {1,2,4,8,10,16,20} U {2,6,8,10,14,18)
AUB = {1,2,4,8,10,14,16,18,20)
U-(AUB)= (1,2,3 ....... 20} - { 1,2,4,8,10,14,16,18,20}
∴ (AUB)' = (5,6,7,9,11,12,13,14,15,17,19) ........ (1)
For R.H.S:
A'∩B'
A' = U - A = (1,2,3,4,5 ........ 20) - (1,2,4,8,10,16,20)
A' = {3,5,6,7,9,11,12,13,14,15,17,18,19}
B' = U - B = (1,2,3,4,5 ...... 20) - {2,4,6,8,10,14,18}
B' = {1,3,5,7,9,11,12,13,15,16,17,19}
A'∩B' = (3,5,6,7,9,11,12,13,14,15,17,18,19) ∩ (1,3,5,7,9,11,12,13,15,16,17,19)
A'∩B' = (5,6,7,9,11,12,13,14,15,17,19) ....... (2)
By (1) and (2)

(AUB)' = A'∩B'

Hence De Morgan's Laws has proved

2. A'UB' = (A∩B)'
Solution:
For L.H.S:
A'UB'
A' = U - A = (1,2,3,4,5 ........ 20) - (1,2,4,8,10,16,20)
A' = {3,5,6,7,9,11,12,13,14,15,17,18,19}
B' = U - B = (1,2,3,4,5 ...... 20) - {2,4,6,8,10,14,18}
B' = {1,3,5,7,9,11,12,13,15,16,17,19,20}
A'UB' = (3, 5, 6, 7, 9, 11, 12, 13, 14, 15, 17, 18, 19) U (1, 3, 5, 7, 9, 11, 12, 13, 15, 16, 17, 19,20}
∴ A'UB' = {1, 3, 5, 6, 7, 9, 11, 12, 13,1 4, 15, 16, 17, 18, 19, 20) ........ (1)
FOR R.H.S
(A∩B)'
A∩B = (1,2,4, 8, 10, 16, 20) ∩ {2, 4, 6, 8, 10, 14, 18}
A∩B = (2,4,8,10)
(A∩B)' = U- (A∩B)
U- (A∩B) = {1, 2, 3 ......... 20} - {2, 4, 8, 10}
∴ (A∩B)' = (1, 3, 5, 6, 7, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20) ....... (2)
By (1) and (2)

A'UB' = (A∩B)'

Hence De Morgan's Laws has proved

(21) Verify the commutative property of union and intersection for the following sets.
(a) A = {1, 2, 3, 4, 5}, B = {3, 5, 7, 9}
(b) A=(x|x ∈ Z+ and x ≤ 5) B = {x|x ∈ Z and l ≤ x ≤ 4}

(a) A = {1, 2, 3, 4, 5}, B = {3, 5, 7, 9}
Solution:
Commutative property of Union is

AUB = BUA

Taking L.H.S:
AUB = {1,2,3,4,5) U {3,5,7,9)
AUB = (1,2,3,4,5,7,9) ........ (1)
Taking R.H.S:
BUA = (3,5,7,9) U (1,2,3,4,5)
BUA = (1,2,3,4,5,7,9) .......... (2)
By (1) and (2)

AUB = BUA Hence Proved

Commutative property for intersection is

A∩B = B∩A

Taking L.H.S:
A∩B = {1,2,3,4,5} ∩ {3,5,7,9}
A∩B = (3,5) .......... (1)
Taking R.H.S:
B∩A = (3,5,7,9) ∩ (1,2,3,4,5)
B∩A = {3,5} ........ (2)
By (1) and (2)

A∩B = B∩A Hence Proved.

(b) A = (x|x ∈ Z+ and x ≤ 5) B = {x|x ∈ Z and l ≤ x ≤ 4}
Solution:
In tabular form:
A = {1,2,3,4,5}
B = {1,2,3,4}
Commutative property of union:

AUB = BUA

Taking L.H.S:
AUB = ( 1,2,3,4,5) U (1,2,3,4)
AUB = { 1,2,3,4,5) ....... (1)
Taking R.H.S:
BUA = (1,2,3,4) U (1,2,3,4,5)
BUA = (1,2,3,4,5) ........ (2)
By (1) and (2)

AUB = BUA Hence Proved.

Commutative property of intersection:

A∩B = B∩A

Taking L.H.S:
A∩B = {1,2,3,4,5) ∩ ( 1,2,3,4)
A∩B = {1,2,3,4) ....... (1)
Taking R.H.S:
A∩B = (1,2,3,4) ∩ ( 1,2,3,4,5)
A∩B = (1,2,3,4) .......... (2)
By (1) and (2)

A∩B = B∩A Hence proved

(22) Verify the following properties for the sets given below:
(i) Associative property of union and of intersection.
(ii) Distributive property of union over intersection.
(iii) Distributive property of intersection over union.
(a) A = {1, 2, 3, 4, 5}, B = {2, 4, 6, 8}, C = {4, 8, 10, 12,}
(b) A = {x|x ∈ Z+ and x ≤ 4}, B = {x|x ∈ Z and 0 < x < 5}, C = {1,2,3}

(a) A = (1,2,3,4,5), B = {2,4,6,8}; c = {4,8,10,12)
Solution:
(i) Associative property of union and of intersection:
Associative property of union

 AU(BUC) = (AUB) UC

Taking L.H.S:
AU(BUC)
BUC = (2,4,6,8) U (4,8,10,12)
BUC = (2,4,6,8,10,12)
AU(BUC) = (1,2,3,4,5) U (2,4,6,8,10,12)
AU(BUC) = (1,2,3,4,5,6,8,10,12) ........ (1)
Taking R.H.S:
(AUB) UC
AUB = (1,2,3,4,5) U (2,4,6,8)
AUB = (1,2,3,4,5,6,8)
(AUB)UC = (1,2,3,4,5,6,8) U (4,8,10,12)
(AUB)UC = (1,2,3,4,5,6,8,10,12) ......... (2)
By (1) and (2)

AU(BUC) = (AUB) UC Hence Proved

Associative property of intersection

A∩(B∩C) = (A∩B) ∩ C

Taking L.H.S:
A∩(B∩C)
B∩C = (2,4,6,8) ∩ (4,8,10,12)
B∩C = (4,8)
A∩(B∩C) = (1,2,3,4,5) ∩ (4,8)
A∩(B∩C) = (4) ........ (1)
Taking R.H.S:
(A∩B) ∩ C
A∩B = (1,2,3,4,5) ∩ (2,4,6,8)
A∩B = (2,4)
(A∩B)∩C = (2,4) ∩ (4,8,10,12)
(A∩B)∩C = (4) ......... (2)
By (1) and (2)

A∩(B∩C) = (A∩B) ∩ C Hence Proved

(ii) Distributive property of union over intersection:

AU(B∩C) = (AUB) ∩ (AUC)

Taking L.H.S:
AU(B∩C)
B∩C = (2,4,6,8) ∩ (4,8,10,12)
B∩C = (4,8)
AU(B∩C)= '{1,2,3,4,5} U {4,8}
AU(B∩C) = {1,2,3,4,5,8} ........ (1)
Taking R.H.S
(AUB) ∩ (AUC)
AUB = {1,2,3,4,5) U {2,4,6,8}
AUB = {1,2,3,4,5,6,8}
AUC = {1,2,3,4,5} U {4,8,10,12}
AUC = {1,2,3,4,5,8,10,12}
(AUB) ∩ (AUC) = {1,2,3,4,5,6,8} ∩ (1,2,3,4,5,8,10,12)
(AUB) ∩ (AUC) = {1,2,3,4,5,8) ....... (2)
By (1) and (2)

AU(B∩C) = (AUB) ∩ (AUC) Hence Proved

(iii) Distributive property of intersection over union:

A∩(BUC) = (A∩B) U (A∩C)

Taking L.H.S:
A∩(BUC)
BUC = {2,4,6,8} U {4,8,10,12}
BUC = {2,4,6,8,10,12}
A∩(BUC) = (1,2,3,4,5} ∩ {2,4,6,8,10,12}
A∩(BUC) = {2,4} ....... (1)
Taking R.H.S:
(A∩B) U (A∩C)
A∩B = {1,2,3,4,5} ∩ {2,4,6,8}
A∩B = {2,4)
A∩C = {1,2,3,4,5} ∩ {4,8,10,12}
A∩C = {4}
(A∩B) U (A∩C) = {2,4} U {4}
(A∩B) U (A∩C) = {2,4} ....... (2)
By (1) and (2)

A∩(BUC) = (A∩B) U (A∩C) Hence Proved.

(b) A = {x|x ∈ Z+ and x ≤ 4}, B = {x|x ∈ Z and 0 < x < 5}, C = {1,2,3}
Solution:
In Tabular Form:
A = {1,2,3,4}
B = {1,2,3,4}
C = {1,2,3}

(i) Associative property of union and of intersection:
Associative property of union

AU(BUC) = (AUB) UC

Taking L.H.S:
AU(BUC)
BUC = {1,2,3,4} U {1,2,3}
BUC = (1,2,3,4)
AU(BUC) = {1,2,3,4} U (1,2,3,4)
AU(BUC) = (1,2,3,4) ........ (1)
Taking R.H.S:
(AUB) UC
AUB = (1,2,3,4) U (1,2,3,4)
AUB = (1,2,3,4)
(AUB)UC = (1,2,3,4) U {1,2,3}
(AUB)UC = {1,2,3,4} ......... (2)
By (1) and (2)

AU(BUC) = (AUB) UC Hence Proved

Associative property of intersection

A∩(B∩C) = (A∩B) ∩ C

Taking L.H.S:
A∩(B∩C)
B∩C = {1,2,3,4} ∩ (1,2,3)
B∩C = (1,2,3)
A∩(B∩C) = (1,2,3,4) ∩ (1,2,3)
A∩(B∩C) = (1,2,3) ........ (1)
Taking R.H.S:
(A∩B) ∩ C
A∩B = (1,2,3,4) ∩ (1,2,3,4)
A∩B = (1,2,3,4)
(A∩B)∩C = (1,2,3,4) ∩ (1,2,3)
(A∩B)∩C = (1,2,3) ......... (2)
By (1) and (2)

A∩(B∩C) = (A∩B) ∩ C Hence Proved

(ii) Distributive property of union over intersection:

AU(B∩C) = (AUB) ∩ (AUC)

Taking L.H.S:
AU(B∩C)
B∩C = (1,2,3,4) ∩ (1,2,3)
B∩C = (1,2,3)
AU(B∩C)= '{1,2,3,4} U {1,2,3}
AU(B∩C) = {1,2,3,4} ........ (1)
Taking R.H.S
(AUB) ∩ (AUC)
AUB = {1,2,3,4) U {1,2,3,4}
AUB = {1,2,3,4}
AUC = {1,2,3,4} U {1,2,3}
AUC = {1,2,3,4}
(AUB) ∩ (AUC) = {1,2,3,4} ∩ (1,2,3,4)
(AUB) ∩ (AUC) = {1,2,3,4) ....... (2)
By (1) and (2)

AU(B∩C) = (AUB) ∩ (AUC) Hence Proved

(iii) Distributive property of intersection over union:

A∩(BUC) = (A∩B) U (A∩C)

Taking L.H.S:
A∩(BUC)
BUC = {1,2,3,4} U {1,2,3}
BUC = {1,2,3,4)
A∩(BUC) = (1,2,3,4} ∩ {1,2,3,4}
A∩(BUC) = {1,2,3,4} ....... (1)
Taking R.H.S:
(A∩B) U (A∩C)
A∩B = {1,2,3,4} ∩ {1,2,3,4}
A∩B = {1,2,3,4}
A∩C = {1,2,3,4} ∩ {1,2,3}
A∩C = {1,2,3}
(A∩B) U (A∩C) = {1,2,3,4} U {1,2,3}
(A∩B) U (A∩C) = {1,2,3,4} ....... (2)
By (1) and (2)

A∩(BUC) = (A∩B) U (A∩C) Hence Proved.