∼(p↔q) is equivalent to - Vidyadip

MCQ

∼(p↔q) is equivalent to

✓
$(p \wedge \sim q) \vee(q \wedge \sim p)$
B
$(p \vee-q) \wedge(q \vee \sim p)$
C
$(p \rightarrow q) \wedge(q \rightarrow p)$
D
$(q \rightarrow p) \vee(p \rightarrow q)$

✓

Answer

Correct option: A.

$(p \wedge \sim q) \vee(q \wedge \sim p)$

(A)
We know that,
$p \leftrightarrow q \equiv(p \rightarrow q) \wedge(q \rightarrow p)$
$\therefore \quad \sim(p \leftrightarrow q) \equiv \sim[(p \rightarrow q) \wedge(q \rightarrow p)]$
$\equiv \sim(p \rightarrow q) \vee \sim(q \rightarrow p)…[By Demorgan's Law]$
$\begin{aligned} \equiv(p \wedge \sim q) & \vee(q \wedge \sim p) \\ & \quad \ldots[\because \sim(p \rightarrow q) \equiv p \wedge \sim q]\end{aligned}$

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