QJEEM23Maf318: JEE Main 2023 Mathematics - Class 11 JEEM23Maf318 Solution: The statement is

Question

Verified Solution • 2025–26 Session moderate

The statement $\left( {p \wedge \left( { \sim q} \right)} \right) \Rightarrow \left( {p \Rightarrow \left( { \sim q} \right)} \right)$ is

Accepted Answer

Making truth table (Let $(p \wedge \sim q) \Rightarrow(p \Rightarrow \sim q)=E$ )

$p$	$q$	$\sim p$	$\sim q$	$p \wedge \sim q$	$p \Rightarrow \sim q$	$E$
$\mathrm{T}$	$\mathrm{T}$	$\mathrm{F}$	$\mathrm{F}$	$\mathrm{F}$	$\mathrm{F}$	$\mathrm{T}$
$\mathrm{T}$	$\mathrm{F}$	$\mathrm{F}$	$\mathrm{T}$	$\mathrm{T}$	$\mathrm{T}$	$\mathrm{T}$
$\mathrm{F}$	$\mathrm{T}$	$\mathrm{T}$	$\mathrm{F}$	$\mathrm{F}$	$\mathrm{T}$	$\mathrm{T}$
$\mathrm{F}$	$\mathrm{F}$	$\mathrm{T}$	$\mathrm{T}$	$\mathrm{F}$	$\mathrm{T}$	$\mathrm{T}$

$\therefore E$ is a tautology

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