Question

$\left[\right(\sim p)\Rightarrow p]\wedge [p\Rightarrow (\sim p\left)\right]$ is

• A. a tautology.
• B. a contradiction.
• C. a tautology and a contradiction.
• D. neither a tautology nor a contradiction.

Answer 1

The correct option is B a contradiction.

$p$	$\sim p$	$\sim p\Rightarrow p$	$p\Rightarrow \sim p$	$(\sim p\Rightarrow p)\wedge (p\Rightarrow \sim p)$
T	F	T	F	F
F	T	F	T	F

From the above table, the truth value of the expression $(\sim p\Rightarrow p)\wedge (p\Rightarrow \sim p)$ is always F. Hence it's a contradiction.