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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