The contrapositive of $(\sim \mathrm{p} \wedge \mathrm{q}) \rightarrow(\mathrm{q} \wedge \sim \mathrm{r})$ is

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

Solution

Contrapositive of $\mathrm{p} \rightarrow \mathrm{q}$ is $\sim \mathrm{q} \rightarrow \sim \mathrm{p}$ Hence, contrapositive of $(\sim p \wedge q) \rightarrow(q \wedge \sim r)$ is $\begin{aligned} & \sim(\mathrm{q} \wedge \sim \mathrm{r}) \rightarrow \sim(\sim \mathrm{p} \wedge \mathrm{q}) \\ & \Rightarrow(\sim \mathrm{q} \vee \mathrm{r}) \rightarrow(\mathrm{p} \vee \sim \mathrm{q})\end{aligned}$

Asked in: MHT CET 2022 (06 Aug Shift 1)

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