Question

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

$p$	$q$	$\sim p$	$p\to q$	$\sim p\to q$	$(\sim p\to q)\to q$	Question
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

Since all the values in the last column are true, hence the given statement is a tautology.