Question

The proposition $p\to \sim (p\wedge \sim q)$ is equivalent to

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

Answer 1

The correct option is D $(\sim p)\vee q$

$p\to \sim (p\wedge \sim q)$
$=\sim p\vee \sim (p\wedge \sim q)$
$=\sim p\vee (\sim p\vee q)$
$=\sim p\vee q$