The negation of inverse of $\sim p \rightarrow q$ is

The negation of inverse of $\sim p \rightarrow q$ is
  1. $\sim \mathrm{p} \wedge \mathrm{q}$
  2. $\sim \mathrm{q} \rightarrow \mathrm{p}$
  3. $p \wedge(\sim q)$
  4. $\mathrm{p} \wedge \mathrm{q}$

Solution

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 $\sim(p \rightarrow \sim q)$ $\equiv \sim(\sim p \vee \sim q) \equiv p \wedge q$

Asked in: MHT CET 2021 (24 Sep Shift 1)

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