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Consider the following Boolean expression for F

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 ) PR + PRS + P

Answer

Here we are given F ( P,Q, R,S ) = PQ + PQR + PQRS

= PQ +P'Q(R+R'S)

Using A + BC = (A + B)(A + C) , we get

F ( P,Q, R,S ) = PQ + P'Q(R + R')(R + S)
= PQ + P'Q(R + S)  [Since R+R' = 1]
= Q(P + P'(R + S))

Again using A + BC = (A + B)(A + C) , we get

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

ANSWER : ( A ) PQ + QR + QS

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