Question

$(\sim p\wedge q)$ is logically equivalent to

• A. $p\to q$
• B. $q\to p$
• C. $\sim \left(p\underset{}{\overset{}{\to }}q\right)$
• D. $\sim \left(q\underset{}{\overset{}{\to }}p\right)$

Answer 1

The correct option is D $\sim \left(q\underset{}{\overset{}{\to }}p\right)$

$\neg (q\to p)\iff \neg (p\vee \neg q)$ Implication Law

$\iff \neg p\wedge \neg \neg q$ De Morgan’s Law

$\iff \neg p\wedge q$ Double Negation Law

$(\neg p\wedge q)$ is logically equivalent to $\neg (q\to p)$