Search any question & find its solution
Question:
Answered & Verified by Expert
The inverse of the statement $(\mathrm{p} \wedge \sim \mathrm{q}) \rightarrow \mathrm{r}$ is
Options:
Solution:
1760 Upvotes
Verified Answer
The correct answer is:
$(\sim \mathrm{p} \vee \mathrm{q}) \rightarrow \sim \mathrm{r}$
The inverse of the proposition $(\mathrm{p} \wedge \sim \mathrm{q})$ $\rightarrow \mathrm{r}$ is
$$
\begin{aligned}
\sim(\mathrm{p} \wedge \sim \mathrm{q}) \rightarrow \sim \mathrm{r} \equiv \sim \mathrm{p} \vee \sim(\sim \mathrm{q}) & \rightarrow \sim \mathrm{r} \\
& \equiv \sim \mathrm{p} \vee \mathrm{q} \rightarrow \sim \mathrm{r}
\end{aligned}
$$
$$
\begin{aligned}
\sim(\mathrm{p} \wedge \sim \mathrm{q}) \rightarrow \sim \mathrm{r} \equiv \sim \mathrm{p} \vee \sim(\sim \mathrm{q}) & \rightarrow \sim \mathrm{r} \\
& \equiv \sim \mathrm{p} \vee \mathrm{q} \rightarrow \sim \mathrm{r}
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.