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The negation of inverse of $\sim p \rightarrow q$ is
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Verified Answer
The correct answer is:
$\mathrm{p} \wedge \mathrm{q}$
We have $\sim \mathrm{p} \rightarrow \mathrm{q}$
Inverse of given statement is
$$
\sim(\sim \mathrm{p}) \rightarrow \sim \text { q i.e. } \mathrm{p} \rightarrow \sim \mathrm{q}
$$
Negation of inverse of given statement is $\sim(p \rightarrow \sim q)$
$$
\equiv \sim(\sim p \vee \sim q) \equiv p \wedge q
$$
Inverse of given statement is
$$
\sim(\sim \mathrm{p}) \rightarrow \sim \text { q i.e. } \mathrm{p} \rightarrow \sim \mathrm{q}
$$
Negation of inverse of given statement is $\sim(p \rightarrow \sim q)$
$$
\equiv \sim(\sim p \vee \sim q) \equiv p \wedge q
$$
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