GATE | GATE CS 2008 | Question 33

P and Q are two propositions. Which of the following logical expressions are equivalent?

(A) Only I and II
(B) Only I, II and III
(C) Only I, II and IV
(D) All of I, II, III and IV

Answer: (B)

Explanation: I and II are same by Demorgan’s law

The IIIrd can be simplified to I.

$\newline \equiv P \wedge (Q \vee \neg Q)\vee(\neg P \wedge \neg Q) \newline \equiv P \vee (\neg P \wedge \neg Q) \newline \equiv (P \vee \neg P) \wedge (P \vee \neg Q) = (P \vee \neg Q)$ since $P\vee \neg P$ is true always

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