The negation of the inverse of the statement | vedclass

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(B) Step $1$: The given statement is $S = \sim p \lor q$.Step $2$: The inverse of a statement $A \implies B$ is $\sim A \implies \sim B$. However, for

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$\sim p \land q$

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(B) Step $1$: The given statement is $S = \sim p \lor q$.Step $2$: The inverse of a statement $A \implies B$ is $\sim A \implies \sim B$. However, for a statement $S$, the inverse is defined as $\sim S$. Thus, the inverse is $\sim(\sim p \lor q) = p \land \sim q$.Step $3$: The negation of the inverse is $\sim(p \land \sim q)$.Step $4$: Using De Morgan's Law, $\sim(p \land \sim q) = \sim p \lor \sim(\sim q) = \sim p \lor q$.Wait, re-evaluating the standard definition: The inverse of $p \implies q$ is $\sim p \implies \sim q$. For the statement $\sim p \lor q$, which is equivalent to $p \implies q$, the inverse is $\sim p \implies \sim q$, which is equivalent to $p \lor \sim q$. The negation of this is $\sim(p \lor \sim q) = \sim p \land q$. Therefore, the correct option is $B$.

The negation of the inverse of the statement $\sim p \lor q$ is...

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