Question

The logical statement $(p\Rightarrow q)\wedge (q\Rightarrow \sim p)$ is equivalent to

• A. $\sim p$
• B. $p$
• C. $q$
• D. $\sim q$

Answer 1

The correct option is A $\sim p$

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

Clearly, $(p\Rightarrow q)\wedge (q\Rightarrow \sim p)$ is equivalent to $\sim p$