Question

The statement $p\Rightarrow \sim q$ is equivalent to

• A. $q\Rightarrow p$
• B. $\sim q\Rightarrow p$
• C. $\sim q\vee \sim p$
• D. $\sim p\vee q$

Answer 1

The correct option is C

$\sim q\vee \sim p$

$p\Rightarrow q$ is false only when p is true and q is false.
$p\Rightarrow \sim q$ is false when p is true and ~q is false i.e. when both p and q are true.

It can be seen that $\sim q\vee \sim p$ is false only when p and q are both true. Hence it is the equivalent of $p\Rightarrow q$