Question

If the Boolean expression $(p\Rightarrow q)\iff (q*(~P\left)\right)$is a tautology, then the Boolean expression $p*(~q)$ is equivalent to:

• A. $p\Rightarrow ~q$
• B. $p\Rightarrow q$
• C. $q\Rightarrow p$
• D. $~q\Rightarrow p$

Answer 1

The correct option is C

$q\Rightarrow p$

Explanation for the correct option.

The table for boolean expression $(p\Rightarrow q)\iff (q*(~P\left)\right)$ is:

$$\begin{gathered} ~(~\mathrm{q}\wedge \mathrm{p})=\mathrm{q}\vee ~\mathrm{p} \\ =~\mathrm{p}\vee \mathrm{q} \\ *\mathrm{is}\mathrm{equivalent}\mathrm{to}\vee \\ =~\mathrm{q}\vee \mathrm{p} \\ =\mathrm{q}\Rightarrow \mathrm{p} \end{gathered}$$

Hence, option C is correct.