The inverse of $p \rightarrow(q \rightarrow r)$ is logically equivalent to

The inverse of $p \rightarrow(q \rightarrow r)$ is logically equivalent to
  1. $\mathrm{p} \rightarrow(\mathrm{q} \rightarrow \mathrm{r})$
  2. $(\mathrm{q} \rightarrow \mathrm{r}) \rightarrow \sim \mathrm{p}$
  3. $(p \vee q) \rightarrow r$
  4. $(\mathrm{q} \rightarrow \mathrm{r}) \rightarrow \mathrm{p}$

Solution

Inverse of $p \rightarrow(q \rightarrow r)$ is $\begin{aligned} & \equiv \sim p \rightarrow \sim(q \rightarrow r) \\ & \equiv(q \rightarrow r) \rightarrow p \end{aligned}$ $\ldots[\because q \rightarrow p \equiv \sim p \rightarrow q]$

Asked in: MHT CET 2024 (10 May Shift 1)

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