The contrapositive of the inverse of $\mathrm{p} \rightarrow(\mathrm{p} \rightarrow \mathrm{q})$ is

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

Solution

Inverse of $p \rightarrow(p \rightarrow q)$ is $\sim \mathrm{p} \rightarrow \sim(\mathrm{p} \rightarrow \mathrm{q})$
Contrapositive of inverse of $p \rightarrow(p \rightarrow q)$ is $\begin{aligned} & \sim[\sim(p \rightarrow q)] \rightarrow \sim(\sim p) \\ & \equiv(p \rightarrow q) \rightarrow p \\ & \equiv(\sim p \vee q) \rightarrow p \end{aligned}$

Asked in: MHT CET 2024 (15 May Shift 2)

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