QJEEM22Ma0a27: JEE Main 2022 Mathematics - Class 11 JEEM22Ma0a27 Solution: The statement is :

Question

Verified Solution • 2025–26 Session moderate

The statement $(\sim(\mathrm{p} \Leftrightarrow \,\sim \mathrm{q})) \wedge \mathrm{q}$ is :

Accepted Answer

$\sim$ (p $\Leftrightarrow$ $\sim$ q) $\wedge$ q

= (p $\Leftrightarrow$ q) $\wedge$ q

p	q	p $\leftrightarrow$ q	(p $\to$ q) $\wedge$ q	(p $\to$ q)	(p $\to$ q) $\wedge$ q	(p $\to$ q) $\wedge$ p
T	T	T	T	T	T	T
T	F	F	F	F	F	F
F	T	F	F	T	T	F
F	F	T	F	T	F	F

$\therefore$ ( $\sim$ (p $\Leftrightarrow$ $\sim$ q)) $\wedge$ q is equivalent to (p $\Rightarrow$ q) $\wedge$ p.

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