Proposition left( { ∼ p} right) vee left( {p, wedge ∼ q} right)

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Mathematical Reasoning

hard

The proposition $\left( { \sim p} \right) \vee \left( {p\, \wedge \sim q} \right)$

A

$p \wedge \left( { \sim q} \right)$

B

$p \to \sim q$

C

$q \to p$

D

$p \vee \left( { \sim q} \right)$

(JEE MAIN-2017)

Solution

$\left( b \right)\,\,\,\,\,\,\,\left( { \sim p} \right) \vee \left( {p \wedge \sim q} \right)$

$p$	$q$	${ \sim p}$	${ \sim q}$	${p \wedge \sim q}$	$\left( { \sim p} \right) \vee \left( {p \wedge \sim q} \right)$
$T$	$T$	$F$	$F$	$F$	$F$
$T$	$F$	$F$	$T$	$T$	$T$
$F$	$T$	$T$	$F$	$F$	$F$
$F$	$F$	$T$	$T$	$F$	$F$

Standard 11

Mathematics

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