GATE | GATE CS 2008 | Question 26

If P, Q, R are Boolean variables, then (P + Q’)(PQ’ + PR)(P’R’ + Q’) simplifies

(A) PQ’
(B) PR’
(C) PQ’ + R
(D) PR” + Q

Answer: (A)
Explanation: Step by step explanation :

= (P + Q’)(PQ’ + PR)(P’R’ + Q’)
= (PPQ’ + PPR + PQ’Q’ + PQ’R) (P’R’ + Q’) 
= (PQ’ + PR + PQ’ + PQ’R) (P’R’ + Q’)
= (PP’Q’R’ + PP’R’R + PP’Q’R’ + PP’Q’RR’ + PQ’Q’ + PQ’R + PQ’Q’ + PQ’Q’R)
= (0 + 0 + 0 + 0 + PQ’ + PQ’R + PQ’ + PQ’R)
= PQ’ + PQ’R
= PQ'(1 + R)
= PQ’ 

So, option (A) is correct.

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