If P, Q, R are Boolean variables, then (P + ~P*Q + ~P*~Q*R) simplifies to A. P*Q B. P + Q C. P*Q*R D. P + Q + R

GATE 2008 · Digital Logic · Boolean Algebra · easy

Answer: P + P'Q + P'Q'R simplifies to P + Q + R. Answer: D.

1. Apply redundancy theorem to first two terms: P + P'Q = P + Q (by redundancy theorem, since P + P' = 1, so P + P'Q = P + Q) Expression becomes: (P + Q) + P'Q'R
2. Simplify (P + Q) + P'Q'R: Note that (P+Q)' = P'Q' by De Morgan's law. So (P + Q) + (P + Q)'*R = (P + Q) + R (redundancy theorem again) Result: P + Q + R