Question

The statement $\sim (p\leftrightarrow \sim q)$ is

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

Answer 1

The correct option is A equivalent to $p\leftrightarrow q$

$\begin{array}{cccccccc}p& q& \sim p& \sim q& p\leftrightarrow q& p\leftrightarrow \sim q& \sim p\leftrightarrow q& \sim (p\leftrightarrow \sim q)\\ T& F& F& T& F& T& T& F\\ F& T& T& F& F& T& T& F\\ T& T& F& F& T& F& F& T\\ F& F& T& T& T& F& F& T\end{array}$
Hence, $\sim (p\leftrightarrow \sim q)isequivalentto(p\leftrightarrow q)$.