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Mathematical Reasoning
medium
The negation of the Boolean expression $((\sim q) \wedge p) \Rightarrow((\sim p) \vee q)$ is logically equivalent to
A
$p \Rightarrow q$
B
$q \Rightarrow p$
C
$\sim(p \Rightarrow q)$
D
$\sim(q \Rightarrow p)$
(JEE MAIN-2022)
Solution
$\sim p \vee q \equiv p \rightarrow q$
$\sim q \wedge p \equiv \sim( p \rightarrow q )$
Negation of $\sim( p \rightarrow q ) \rightarrow( p \rightarrow q )$
is $\sim(p \rightarrow q) \wedge(\sim(p \rightarrow q))$
i.e. $\sim(p \rightarrow q)$
Standard 11
Mathematics
