Consider the following Boolean expression of a function F: F(P,Q) = (P' + Q) XOR (P'Q). Which of the

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Question

Consider the following Boolean expression of a function F: F(P,Q) = (P' + Q) XOR (P'Q). Which of the following expressions is/are equivalent to F?(A) NOT(P' XOR Q') (B) P XOR Q (C) P' XOR Q (D) P' XOR Q'

Accepted Answer

Correct Answer: (A) and (C)Concept -- Boolean Algebra and Truth Table Verification: F(P,Q) = (P'+Q) XOR (P'Q). Evaluate for all four combinations: P=0,Q=0: (1+0)=1, (1·0)=0 → 1 XOR 0 = 1. P=0,Q=1: (1+1)=1, (1·1)=1 → 1 XOR 1 = 0. P=1,Q=0: (0+0)=0, (0·0)=0 → 0 XOR 0 = 0. P=1,Q=1: (0+1)=1, (0·1)=0 → 1 XOR 0 = 1. So F = [1,0,0,1]. Check A: NOT(P' XOR Q') = XNOR(P',Q') = (P' = Q'). P=0,Q=0: P'=1,Q'=1 → 1. P=0,Q=1: 1,0 → 0. P=1,Q=0: 0,1 → 0. P=1,Q=1: 0,0 → 1. Matches F. Check C: P' XOR Q: 1 XOR 0=1; 1 XOR 1=0; 0 XOR 0=0; 0 XOR 1=1. Matches F. Check B: P XOR Q gives [0,1,1,0] — not match. D: P' XOR Q' gives [0,1,1,0] — not match. Thus F is equivalent to both (A) and (C). This illustrates the use of truth tables or algebraic manipulation to verify equivalence of Boolean expressions.

Consider the following Boolean expression of a function F: F(P,Q) = (P' + Q) XOR (P'Q). Which of the following expressions is/are equivalent to F?(A) NOT(P' XOR Q') (B) P XOR Q (C) P' XOR Q (D) P' XOR Q'

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Consider the following Boolean expression of a function F: F(P,Q) = (P' + Q) XOR (P'Q). Which of the following expressions is/are equivalent to F?(A) NOT(P' XOR Q') (B) P XOR Q (C) P' XOR Q (D) P' XOR Q'

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