Q76 / 120 · VITEEE 2019 · Mathematics

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

  • A
    $\sim(\mathrm{p} \vee \sim \mathrm{q}) \rightarrow \sim \mathrm{r}$
  • B
    $(\sim \mathrm{p} \wedge \mathrm{q}) \rightarrow \sim \mathrm{r}$
  • Correct answer
    C
    $(\sim \mathrm{p} \vee \mathrm{q}) \rightarrow \sim \mathrm{r}$
  • D
    None of these

Solution

The inverse of the proposition $(\mathrm{p} \wedge \sim \mathrm{q})$ $\rightarrow \mathrm{r}$ is $$ \begin{aligned} \sim(\mathrm{p} \wedge \sim \mathrm{q}) \rightarrow \sim \mathrm{r} \equiv \sim \mathrm{p} \vee \sim(\sim \mathrm{q}) & \rightarrow \sim \mathrm{r} \\ & \equiv \sim \mathrm{p} \vee \mathrm{q} \rightarrow \sim \mathrm{r} \end{aligned} $$

Hence, the correct answer is option: 'C'.

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