ISRO | ISRO CS 2008 | Question 1

The Boolean expression Y = (A + B’ + A’B)C’ is given by
(A) AC’
(B) BC’
(C) C’
(D) AB

Answer: (C)
Explanation:

Y = (A + B' + A'B)C'
Y = AC' + B'C' + A'BC'
Y = AC'+ A'BC' + B'C'
Y = (A + A'B)C' + B'C' // Distributive property
Y = ((A + A')(A + B))C' + B'C' 
Y = AC'+ BC' + B'C'
Y = AC'+ (B + B')C'
Y = AC'+ C'
Y = C'(A + 1) // 1 + A = 1
Y = C'

Option (C) is correct.

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