Computer Studies For Class IX (Science) and X (Arts /General /Humanities Group) - Unit 6 -Videos Expalanations- By Sir Moin

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Chapter No.6: Boolean Algebra
Videos Expalanations

By Sir Moin

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 Boolean Algebra Rule # 10

Rule 10: A + A.B = A

Proof:
This rule can be proved by applying the distributive law, rule 2 and rule 4 as follows.

A + B	= A(1 + B)	Factoring A (Distributive law)
	= A.1	Rule 2: B + 1 = 1
	= A	Rule 4: A.1= A

The proof is shown in the Truth table.

A	B	A.B	A + A.B
0	0	0	0
0	1	0	0
1	0	0	1
1	1	1	1

|-------------------------------------Equal-----------------------------------|

 Boolean Algebra Rule # 11

Rule 11: A + A.B = A + B

Proof:
This rule can be proved as.

A + A.B	= (A + A.B) + A.B	Rule 10: A = A + A.B
	= (AA + AB) + AB	Rule 6: A = AA
	= AA + AB + AA + AB	Rule 8: Adding AA = 0
	= (A +  A) (A + B)	Factoring
	= 1 . (A + B)	Rule 7: A + A= 1
	= (A + B)	Rule 4: Drop 1

The proof is shown in the Truth table.

A	B	AB	A + AB	A + B
0	0	0	0	0
0	1	1	1	1
1	0	0	1	1
1	1	0	1	1

|--------Equal-----|