Question

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

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

Answer 1

The correct option is C $\sim r\Rightarrow (\sim p\wedge \sim q)$

Contrapositive of $p\to q$ is $\sim q\to \sim p$.
$\therefore$ Contrapositive of $(p\vee q)\Rightarrow r$ is $\sim r\Rightarrow \sim (p\vee q)$ i.e. $\sim r\Rightarrow (\sim p\wedge \sim q)$.