Q78 / 180 · COMEDK 2019 · Mathematics
- The converse of the contrapositive of the conditional $p \rightarrow \sim q$ is
- A$p \rightarrow q$
- B$\sim p \rightarrow \sim q$
- C$\sim q \rightarrow p$
- Correct answerD$\sim p \rightarrow q$
Solution
We have,
$$
p \rightarrow \sim q
$$
The contrapositive of $p \rightarrow q$ is $\sim q \rightarrow \sim p$ and converse of $p \rightarrow q$ is $q \rightarrow p$.
$\therefore$ Contrapositive of $p \rightarrow \sim q$ is $\sim(\sim q) \rightarrow \sim p \equiv q \rightarrow \sim p$.
Converse of $q \rightarrow \sim p$ is $\sim p \rightarrow q$.
Hence, the correct answer is option: 'D'.