The converse of $[p \wedge(\sim q)] \rightarrow r$ is

The converse of $[p \wedge(\sim q)] \rightarrow r$ is
  1. $\sim \mathrm{r} \rightarrow(\sim \mathrm{p} \vee \mathrm{q})$
  2. $\mathrm{r} \rightarrow(\sim \mathrm{p} \wedge \sim \mathrm{q})$
  3. $\quad(\sim p \vee q) \rightarrow \sim r$
  4. $\quad \mathrm{r} \rightarrow(\mathrm{p} \wedge \mathrm{q})$

Solution

$\begin{aligned} & \text { Converse of }[p \wedge(\sim q)] \rightarrow r \\ & =\sim[p \wedge(\sim q)] \rightarrow \sim r \\ & =(\sim p \vee q) \rightarrow \sim r \end{aligned}$ ...[De morgans Law]

Asked in: MHT CET 2024 (04 May Shift 2)

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