Question

Simplify the following expression.

Y = AB + A(B + C) + B(B + C)

1. Y = A + B + C
2. Y = B + AC
3. Y = A + BC
4. Y = AB + C

Answer 1

Correct Answer - Option 2 : Y = B + AC

Analysis:

Y = AB + A(B + C) + B(B + C)

= AB + AB + AC + B + BC

Since AB + AB = AB, we get:

Y = AB + AC + B (1 + C)

Since 1 + X (any variable) = X, we get:

Y = AB + AC + B     

Y = B(1 + A) + AC  

Y = B + AC

All Boolean algebra laws are shown below

Name	AND Form	OR Form
Identity law	1.A = A	0 + A = A
Null Law	0.A = 0	1 + A = 1
Idempotent Law	A. A = A	A + A = A
Inverse Law	AA’ = 0	A + A’ = 1
Commutative Law	AB = BA	A + B = B + A
Associative Law	(AB)C	(A + B) + C = A + (B + C)
Distributive Law	A + BC = (A + B) (A + C)	A (B + C) = AB + AC
Absorption Law	A (A + B) = A	A + AB = A
De Morgan’s Law	(AB)’ = A’ + B’	(A + B)’ = A’B’