Question

The proposition $\left(p\Rightarrow ~p\right)\wedge \left(~p\Rightarrow p\right)$ is a

• A. Tautology and contradiction
• B. Neither tautology nor contradiction
• C. Contradiction
• D. Tautology

Answer 1

The correct option is C

Contradiction

Explanation for the correct option:

Given proposition, $\left(p\Rightarrow ~p\right)\wedge \left(~p\Rightarrow p\right)$

Make a truth table

$\begin{array}{|ccccc|}\hline p& ~p& p\Rightarrow ~p& ~p\Rightarrow p& \left(p\Rightarrow ~p\right)\wedge \left(~p\Rightarrow p\right)\\ T& F& F& T& F\\ F& T& T& F& F\\ \hline\end{array}$

$\left(p\Rightarrow ~p\right)\wedge \left(~p\Rightarrow p\right)$ is a contradiction.

Hence, option (C) is the correct answer.