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Mathematical Reasoning
medium
જો $(p \wedge r) \Leftrightarrow(p \wedge(\sim q))$ એ $(\sim p)$ સમકક્ષ હોય, તો $r=$ ........
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
