GATE 2011 CS (CS1) – Question 24
Digital Logic · Boolean Algebra and Minimization · 1 mark · Multiple choice
Simplify $(P+\bar Q+\bar R)(P+\bar Q+R)(P+Q+\bar R)$ to SOP.
- $\bar PQ+\bar R$
- $P+\bar Q\bar R$
- $\bar PQ+R$
- $PQ+R$
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Show answer and explanation
Correct answer: (B) $P+\bar Q\bar R$
Explanation
Combine the first two factors using (X+R̄)(X+R)=X with X=P+Q̄. The result is (P+Q̄)(P+Q+R̄). Applying (P+A)(P+B)=P+AB gives P+Q̄(Q+R̄)=P+Q̄R̄. Thus B.
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