GATE 2015 CS – Question 19

Engineering Mathematics · Discrete Mathematics: Propositional and First Order Logic · 1 mark · Multiple choice

Which one of the following is NOT equivalent to $p \leftrightarrow q$?

$(\neg p \vee q) \wedge (p \vee \neg q)$
$(\neg p \vee q) \wedge (q \rightarrow p)$
$(\neg p \wedge q) \vee (p \wedge \neg q)$
$(\neg p \wedge \neg q) \vee (p \wedge q)$

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Correct answer: (C) $(\neg p \wedge q) \vee (p \wedge \neg q)$

Explanation

$p \leftrightarrow q$ is true when $p$ and $q$ have the same value. Options A, B and D all describe that, since $(\neg p \vee q)$ is $p \rightarrow q$ and $(p \vee \neg q)$ is $q \rightarrow p$. Option C is true when $p$ and $q$ differ, which is $p \oplus q$, the negation of $p \leftrightarrow q$.