Question

The propositions $\left(p\Rightarrow p\right)\wedge \left(\sim p\Rightarrow p\right)$ is a

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

Answer 1

Answer: (C)

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

Clearly, $(p\Rightarrow \sim p)\wedge (\sim p\Rightarrow p)$ is a contradiction.