Question

The proposition $\sim (p\vee \sim q)\vee \sim (p\vee q)$ is logically equivalent to :

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

Answer 1

The correct option is A $\sim p$

$\sim (p\vee \sim q)\vee \sim (p\vee q)$
$=(\sim p\wedge q)\vee (\sim p\wedge \sim q)$ (by Demorgan law)
$=\sim p\wedge (q\vee \sim q)$ (by Distributive property)
$=\sim p$