Question

The proposition $p\Rightarrow ~(p\wedge ~q)$ is

• A. A contradiction
• B. A tautology
• C. Either $A$ or $B$
• D. Neither $A$ nor $B$

Answer 1

The correct option is D

Neither $A$ nor $B$

Explanation for correct option

Given, $p\Rightarrow ~(p\wedge ~q)$

Make a truth table

$\begin{array}{|cccccc|}\hline p& q& ~q& p\wedge ~q& ~(p\wedge ~q)& p\Rightarrow ~(p\wedge ~q)\\ T& T& F& T& T& T\\ T& F& T& F& F& F\\ F& T& F& T& T& T\\ F& F& T& T& T& T\\ \hline\end{array}$

$p\Rightarrow ~(p\wedge ~q)$ is neither tautology nor contradiction

Hence, option (D) is the correct answer.