Question

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

• A. fallacy
• B. tautology
• C. false if either of $p$ or $q$ is false.
• D. true if $p$ is false

Answer 1

The correct option is D true if $p$ is false

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

Hence, the given proposition is neither tautology nor contradiction.