QJEEM21Ma6bbb: JEE Main 2021 Mathematics - Class 11 JEEM21Ma6bbb Solution: If the Boolean expression (p q) (q * ( p) is a tautology, then…

Question

Verified Solution • 2025–26 Session moderate

If the Boolean expression (p

\Rightarrow

q)

\Leftrightarrow

(q * (

\sim

p) is a tautology, then the boolean expression (p * (

\sim

q)) is equivalent to :

Accepted Answer

The Boolean expression

$(p \Rightarrow q) \Leftrightarrow\left(q^*(\sim p)\right)$ is a tautology.

Making the truth table for this

p	q	$p \rightarrow q$	$q^* \sim p$	$\sim q$	$-q \wedge p$	$\sim(\sim {q} \wedge p)$
$\mathrm{T}$	$\mathrm{T}$	$\mathrm{T}$	$\mathrm{T}$	$\mathrm{F}$	$\mathrm{F}$	$\mathrm{T}$
T	F	F	F	T	T	F
F	T	T	T	F	F	T
F	F	T	T	T	F	T

$\therefore \quad \sim(\sim q \wedge p)=q \vee \sim p=\sim p \vee q$

$\therefore{ }^*$ is equivalent to $v$ .

So, $\quad p^* \sim q=p \vee \sim q=\sim q \vee p$

$=q \Rightarrow p$

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