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Mathematical Reasoning
hard
The statement $( p \wedge(\sim q )) \Rightarrow( p \Rightarrow(\sim q ))$ is
A
equivalent to $(\sim p) \vee(\sim q)$
B
a tautology
C
equivalent to $p \vee q$
D
a contradiction
(JEE MAIN-2023)
Solution
$( p \wedge \sim q ) \rightarrow( p \rightarrow \sim q )$
$\equiv(\sim( p \wedge \sim q )) \vee(\sim p \vee \sim q )$
$\equiv(\sim p \vee q ) \vee(\sim p \vee \sim q )$
$\equiv \sim p \vee t \equiv t$
Standard 11
Mathematics
