Question

The Statement $~(p\leftrightarrow ~q)$ is

• A. equivalent to $p\leftrightarrow q$
• B. equivalent to $~p\leftrightarrow q$
• C. a tautology
• D. a fallacy

Answer 1

The correct option is A

equivalent to $p\leftrightarrow q$

The explanation for the correct option:

Given, $~(p\leftrightarrow ~q)$

Make a truth table

$\begin{array}{|cccccccc|}\hline p& q& ~p& ~q& p\leftrightarrow q& p\leftrightarrow ~q& ~p\leftrightarrow q& ~(p\leftrightarrow ~q)\\ T& F& F& T& F& T& T& F\\ F& T& T& F& F& T& T& F\\ T& T& F& F& T& F& F& T\\ F& F& T& T& T& F& F& T\\ \hline\end{array}$

Thus, $~(p\leftrightarrow ~q)$ is equivalent to $p\leftrightarrow q$.

Hence, option (A) is the correct answer.