Question

The logical statement $(p\to q)\to ((\sim p\to q)\to q)$ is

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

Answer 1

The correct option is A a tautology

The truth table of given expression is given below
$\begin{array}{ccccccc}p& q& x\equiv p\to q& \sim p& \sim p\to q& y\equiv (\sim p\to q)\to q& x\to y\\ T& T& T& F& T& T& T\\ T& F& F& F& T& F& T\\ F& T& T& T& T& T& T\\ F& F& T& T& F& T& T\end{array}$

For all possible truth values of $p$ and $q,$ the statement $(p\to q)\to ((\sim p\to q)\to q)$ is true.
Hence, the given statement is a tautology.