Question

The contrapositive statement of the proposition $p\to ~q$ is

• A. $~p\to q$
• B. $~q\to p$
• C. $q\to ~p$
• D. None of these

Answer 1

The correct option is C

$q\to ~p$

Explanation for correct option:

Finding the contrapositive statement of the given proposition:

Given that $p\to ~q$

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

Now, the contrapositive to the above statement will be

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

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

Hence, option (C) is the correct answer