Project ForgeDigital Logic
Boolean Algebra & Minimization
GATE 2008
Expert
If P, Q, R are Boolean variables, then (P+Q̄)(P.Q̄+P.R)(P̄.R̄+Q̄) simplifies to
- P.Q̄
- BP.R̄
- CP.Q̄+R
- DP.R̄+Q
Explanation
P.Q̄+P.R = P(Q̄+R). Since this already requires P=1, ANDing with (P+Q̄) is redundant (P+Q̄ is automatically true whenever P=1) — so the first two factors reduce to P(Q̄+R) = PQ̄+PR. ANDing with the third factor (P̄R̄+Q̄): PQ̄·P̄R̄=0, PQ̄·Q̄=PQ̄, PR·P̄R̄=0, PR·Q̄=PRQ̄. Sum = PQ̄+PRQ̄ = PQ̄ (absorption). Final result: P.Q̄.
Source: GATE CS 2008 (2008)
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