Question

The statement $(p\to q)\to \left[\right(\sim p\to q)\to q]$ is

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

Answer 1

The correct option is A a tautology

$\begin{array}{ccccccc}p& q& \sim p& p\to q& \sim p\to q& (\sim p\to q)\to q& (p\to q)\to \left[\right(\sim p\to q)\to q]\\ T& T& F& T& T& T& T\\ T& F& F& F& T& F& T\\ F& T& T& T& T& T& T\\ F& F& T& T& F& T& T\end{array}$

Clearly, it is a tautology.