Question

Find the correct option for simplification of the Boolean expression.
(P + Q + R)(S + T)' + (P + Q + R)(S + T)
1. P' Q' R'
2. S + T 
3. P + Q + R
4. S' + T'

Answer 1

Correct Answer - Option 3 : P + Q + R

Concept: 

Name of Law	AND Law	OR Law
Identity Law	1 ∙ A = A	0 + A = A
Null Law	0 ∙ A = 0	1 + A = 1
Inverse Law	A ∙ A = A	A + A = A
Idempotent Law	A ∙ A’ = 0	A + A’ = 1
Associative Law	A ∙ B = B ∙ A	A + B = B + A
Distributive Law	(A ∙ B) C = A (B ∙ C)	(A + B) + C = A + (B + C)
Absorption Law	A (A + B) = A	A + A ∙ B = A
De Morgan Law	(A ∙ B)’ = A’ + B’	(A + B)’ = A’ ∙ B’

Calculation:

Given,

F = (P + Q + R)(S + T)' + (P + Q + R)(S + T) .... (1)

Consider, X = (P + Q + R)

Y = (S + T)

Hence, equation (1) becomes,

F = XY' + XY

or, F = X (Y + Y')

From above concept of Idempotent Law,

Y + Y' = 1

Hence, F = X∙1 = X

Hence, F = X = (P + Q + R)