Question

The logical equivalence of the Boolean expression $~\left(\mathrm{p}\wedge ~\mathrm{q}\right)\vee \left(\mathrm{q}\vee ~\mathrm{p}\right)$ is

Answer 1

Compute the required value.

$$\begin{gathered} ~\left(\mathrm{p}\wedge ~\mathrm{q}\right)\vee \left(\mathrm{q}\vee ~\mathrm{p}\right) \\ \equiv \left(~\mathrm{p}\wedge \mathrm{q}\right)\vee \left(\mathrm{q}\vee ~\mathrm{p}\right) \\ \equiv ~\mathrm{p}\vee \mathrm{q} \\ \equiv \mathrm{p}\to \mathrm{q} \end{gathered}$$

Hence the logical equivalence of the Boolean expression $~\left(\mathrm{p}\wedge ~\mathrm{q}\right)\vee \left(\mathrm{q}\vee ~\mathrm{p}\right)$ is $\mathrm{p}\to \mathrm{q}$.