Consider :
$\left(s_1\right):\left(p\Rightarrow q\right)\vee (p\wedge (~q))$  is a tautology
$\left(s_2\right):\left((~p)\Rightarrow (~q)\right)\wedge ((~p)\vee q)$  is a contradiction, then

$\begin{array}{l}{\mathrm{S}}_1:(~\mathrm{p}\vee \mathrm{q})\vee (\mathrm{q}\vee \mathrm{p})=(\mathrm{q}\vee ~\mathrm{p})\vee (\mathrm{q}\vee \mathrm{p})\\ {\mathrm{S}}_1=\mathrm{q}\vee (~\mathrm{p}\vee \mathrm{p})=\mathrm{q}\vee T=T=\text{ tautology }\\ {\mathrm{S}}_2:(\mathrm{p}\wedge ~\mathrm{q})\wedge (~\mathrm{p}\vee \mathrm{q})=(\mathrm{p}\wedge ~\mathrm{q})\wedge ~(\mathrm{p}\wedge ~\mathrm{q})=F=\mathrm{Contradiction}\end{array}$