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Mathematical Reasoning
medium
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
A
$\wedge$
B
$\vee$
C
$\Rightarrow$
D
$\Leftrightarrow$
(JEE MAIN-2022)
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 $C$
$( p \wedge q ) \Rightarrow \sim p \vee q$
$\Rightarrow \sim p \vee \sim q \vee \sim p \vee q$
$\Rightarrow t$
Hence $C$
Standard 11
Mathematics
