Question

Which of the following is logically equivalent to $p \wedge q ?$

• A. $p \rightarrow \sim q$
• B. $\sim p \vee \sim q$
• C. $\sim(p \rightarrow \sim q)$
• D. $\sim\left(\sim p \wedge \sim q^2\right)$

Answer 1

Answer: (C)

We have,
$p \rightarrow q \cong \sim p \vee q$
$\therefore p \rightarrow \sim q \cong \sim p \vee \sim q \cong \sim (p \wedge q)$
So, option (a) is not correct
$\sim p \vee \sim q=\sim(p \wedge q)$
So, option (b) is not correct
$\sim(p \rightarrow \sim q)=\sim(\sim p \vee \sim q)=p \wedge q$
So, option (c) is incorrect