Question

The contrapositive of$(p\vee q)=r$ is

• A. $~r\Rightarrow \left(p\vee q\right)$
• B. $r\Rightarrow \left(p\vee q\right)$
• C. $~r\Rightarrow \left(~p\wedge ~q\right)$
• D. $p\Rightarrow \left(q\vee r\right)$

Answer 1

The correct option is C

$~r\Rightarrow \left(~p\wedge ~q\right)$

Explanation for correct option:

Finding the contrapositive statement:

Given that$(p\vee q)=r$

It means if $p$or $q$ then $r$.

Now the contrapositive of the statement will be

$$\begin{gathered} ~(p\vee q)=~r \\ \Rightarrow ~p\wedge ~q=~r \end{gathered}$$

It means if not $p$ and not $q$ then not $r$

Hence, the correct option is (C).