Mathematical Reasoning
medium

$\left(p^{\wedge} r\right) \Leftrightarrow\left(p^{\wedge}(\sim q)\right)$ is equivalent to $(\sim p)$ when $r$ is.

A

$p$

B

$\sim\,p$

C

$q$

D

$\sim\,q$

(JEE MAIN-2022)

Solution

Given $\left(p^{\wedge} r\right) \Leftrightarrow\left(p^{\wedge}(\sim q)\right) \equiv(\sim p)$

Taking $r = q$

$p$ $q$ $\sim\,p$ $\sim\,q$ $p ^{\wedge} q$ $p ^{\wedge} q$ $\left(p^{\wedge} r\right) \Leftrightarrow\left(p^{\wedge}(\sim q)\right)$
$T$ $T$ $F$ $F$ $T$ $F$ $F$
$T$ $F$ $F$ $T$ $F$ $T$ $F$
$F$ $T$ $T$ $F$ $F$ $F$ $T$
$F$ $F$ $T$ $T$ $F$ $F$ $T$

So, clear $\left(p^{\wedge} r\right) \Leftrightarrow\left(p^{\wedge}(\sim q)\right) \equiv(\sim p)$

Standard 11
Mathematics

Similar Questions

Start a Free Trial Now

Confusing about what to choose? Our team will schedule a demo shortly.