Question

The proposition $(p\to \sim p)\wedge (\sim p\to p)$ is

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

Answer 1

Answer: (B)

The truth table of $(p\to \sim p)\wedge (\sim p\to p)$ is as follows:

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

Clearly, last column of the above truth table contains $F$ only. So, the given statement is a contradiction.