GATE | GATE-CS-2014-(Set-1) | Question 65

Consider the following Boolean expression for F:

F(P, Q, R, S) = PQ + P'QR + P'QR'S

The minimal sum-of-products form of F is
(A) PQ + QR + QS
(B) P + Q + R + S
(C) P’ + Q’ + R’ + S’
(D) P’R + P’R’S + P

Answer: (A)
Explanation: Given,

F(P, Q, R, S) = PQ + P'QR + P'QR'S
= Q(P + P'R + P'R'S)
= Q(P + R + R'S)
= Q(P + R + S)
= PQ + QR + QS

Note that A + AB = A and A + A’B = A + B.

So, option (A) is correct.
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