The Boolean expression
$(\mathrm{p} \Rightarrow \mathrm{q}) \wedge(\mathrm{q} \Rightarrow \sim \mathrm{p})$ is equivalent to :
Correct Option: , 4
$(\mathrm{p} \rightarrow \mathrm{q}) \wedge(\mathrm{q} \rightarrow \sim \mathrm{p})$
$\equiv(\sim \mathrm{p} \vee \mathrm{q}) \wedge(\sim \mathrm{q} \vee \sim \mathrm{p}) \quad\{\mathrm{p} \rightarrow \mathrm{q} \equiv \sim \mathrm{p} \vee \mathrm{q}\}$
$\equiv(\sim \mathrm{p} \vee \mathrm{q}) \wedge(\sim \mathrm{p} \vee \sim \mathrm{q}) \quad\{$ commutative property $\}$
$\equiv \sim \mathrm{p} \vee(\mathrm{q} \wedge \sim \mathrm{q}) \quad\{$ distributive property $\}$
$\equiv \sim \mathrm{p}$
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