Question

The converse of the contrapositive of the conditional $p\to ~q$is

• A. $p\to q$
• B. $~p\to ~q$
• C. $~q\to p$
• D. $~p\to q$

Answer 1

The correct option is D

$~p\to q$

Explanation for correct option:

Finding the converse of the contrapositive of the given condition:

Given that $p\to ~q$

It means that if $p$, then not $q$

Then the contrapositive to the above statement will be

$$\begin{gathered} ~\left(p\to ~q\right) \\ \Rightarrow ~\left(~q\right)\to ~p \\ \Rightarrow q\to ~p\left[\because ~\left(~q\right)=q\right] \end{gathered}$$

Now, the converse of this will be

$\Rightarrow ~p\to q$

It means that if $p$ not then $q$

Hence, option (D) is the correct answer