The inverse of statement pattern $(p \vee q) \rightarrow(p \wedge q)$ is

The inverse of statement pattern $(p \vee q) \rightarrow(p \wedge q)$ is
  1. $(\sim p \vee \sim q) \rightarrow(\sim p \wedge \sim q)$
  2. $(p \wedge q) \rightarrow(p \vee q)$
  3. $(p \wedge q) \rightarrow(p \vee q)$
  4. $\sim(p \vee q) \rightarrow(p \wedge q)$

Solution

$\begin{aligned} & \because \text { inverse of } p \rightarrow q \text { is } \sim p \rightarrow \sim q \\ & \Rightarrow \text { inverse of } p \vee q \rightarrow p \wedge q \\ & \equiv \sim(p \vee q) \rightarrow \sim(p \wedge q) \\ & \equiv(\sim p \wedge \sim q) \rightarrow(\sim p \vee \sim q)\end{aligned}$

Asked in: MHT CET 2022 (11 Aug Shift 1)

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