Question

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

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

Answer 1

The correct option is A $\sim p$

$\sim (p\vee q)\vee (\sim p\wedge q)$
Using Set Theory approach, above statement can be expressed as
$(P\cup Q{)}^c\cup (P^c\cap Q)$
$=(P^c\cap Q^c)\cup (P^c\cap Q)$
$=P^c\cap (Q^c\cup Q)$
$=P^c\cap U$
$=P^c$

Hence, the answer is $\sim p$