Simplify the Boolean expression (P + Q')( PQ' + PR)( P'R' + Q').

If $P$, $Q$, $R$ are Boolean variables, then $(P + Q')( PQ' + PR)( P'R' + Q')$ simplifies to 

(A) $PQ'$ 

(B) $PR'$

(C) $PQ'$ 

(D) $PR' + Q$ 

(GATE 2008) 

Answer: (A) $PQ'$ 

Explanation: 

$(P + Q')( PQ' + PR)( P'R' + Q')$ 

$= (PQ' + PR + PQ' + PQR)(P'R' + Q')$, since $AA = A$ 

$= PQ' + PQ'R + PQ' + PQ'R$, since $AA' = 0$ 

$= PQ' + PQ'R$ 

$= PQ'(1 + R)$ 

$= PQ'$ 

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