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  4. Let Δ ∈ ∧, ∨, ⇒, Leftrightarrow be such that ( p ∧ q ) Δ(( p ∨ q ) ⇒ q ) is a tautology. Then Δ is equal to:

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Q. Let $\Delta \in\{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$ be such that $( p \wedge q ) \Delta(( p \vee q ) \Rightarrow q )$ is a tautology. Then $\Delta$ is equal to:

JEE MainJEE Main 2022Mathematical Reasoning

Solution:

$p \vee q \Rightarrow q$
$\Rightarrow \sim( p \vee q ) \vee q$
$\Rightarrow(\sim p \wedge \sim q ) \vee q$
$\Rightarrow(\sim p \vee q ) \wedge(\sim q \vee q )$
$\Rightarrow(\sim p \vee q ) \wedge t =\sim p \vee q$
Now by taking option $C$
$( p \wedge q ) \Rightarrow \sim p \vee q$
$\Rightarrow \sim p \vee \sim q \vee \sim p \vee q$
$\Rightarrow t$