MHTCET 16 May 2024 Shift 2 Paper

Concept:The given logical statement can be checked using a truth table to see whether it matches any of the given options.Explanation:Construct the truth table columns for $p$, $q$, $\sim q$, $p \leftrightarrow \sim q$, $\sim(p \leftrightarrow \sim q)$, and $p \leftrightarrow q$.

$p$	$q$	$\sim q$	$p \leftrightarrow \sim q$	$\sim(p \leftrightarrow \sim q)$	$p \leftrightarrow q$
$T$	$T$	$F$	$F$	$T$	$T$
$T$	$F$	$T$	$T$	$F$	$F$
$F$	$T$	$F$	$T$	$F$	$F$
$F$	$F$	$T$	$F$	$T$	$T$

The entries in the column for $\sim(p \leftrightarrow \sim q)$ are identical to those in the column for $p \leftrightarrow q$ for every possible combination of truth values.Hence, $\sim(p \leftrightarrow \sim q) \equiv p \leftrightarrow q$.It is not a tautology because not all entries are $T$.It is not a fallacy because not all entries are $F$.It is also not equivalent to $\sim p \leftrightarrow q$.Answer:A. equivalent to $\mathrm{p} \leftrightarrow \mathrm{q}$