Question

The Boolean expression $(p\wedge \sim q)\Rightarrow (q\vee \sim p)$ is equivalent to

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

Answer 1

The correct option is B $p\Rightarrow q$

$\because p\Rightarrow q$ is $\sim p\vee q$
$\therefore (p\wedge \sim q)\Rightarrow (q\vee \sim p)$
$=\sim (p\wedge \sim q)\vee (q\vee \sim p)$
$=(\sim p\vee q)\vee (\sim p\vee q)$
$=\sim p\vee q$
$=p\Rightarrow q$