Question

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

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

Answer 1

The correct option is C $\sim p\wedge \sim q$

We know that
$p\to q\equiv \sim p\vee q$
then $\sim p\to q\equiv p\vee q$
$\sim (\sim p\to q)\equiv \sim (p\vee q)$
$\equiv \sim p\wedge \sim q$