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Simplify the following expression using Boolean laws:
Simplify the following expression using Boolean laws:
$F = PQ + ( P + Q ) \cdot ( P + PR ) + Q$
Answer
Answer
AI$F = PQ + (P+Q)\cdot(P+PR) + Q$
$P+PR = P(1+R) = P$ (since $1+R=1$)
So $(P+Q)\cdot(P+PR) = (P+Q)\cdot P = P$ (Absorption law: $P\cdot(P+Q)=P$)
$F = PQ + P + Q$
$PQ+P = P$ (Absorption law)
$F = P + Q$ (verified with the boolean tool)
Final simplified expression: $F = P+Q$
From ISC 2023 Specimen Computer Science Paper 1, question 4(iii).