The statement \((p \wedge(\sim q) \vee((\sim p) \wedge q) \vee((\sim p) \wedge)(\sim q))\) is equivalent to [JEE Main 20…

\(\begin{aligned} & (p \wedge(\sim q) \vee((\sim p) \wedge q) \vee((\sim p) \wedge)(\sim q)) \\ = & (p \wedge(\sim q)) \vee((\sim p) \wedge(q \vee(\sim q))) \\ = & (p \wedge(\sim q)) \vee((\sim p) \wedge t) \\ = & (p \wedge(\sim q)) \vee(\sim p) \\ = & (\sim p) \vee(p \wedge \sim q) \\ = & (\sim p \vee p) \wedge(\sim p \wedge \sim q) \\ = & t \wedge(\sim p \vee \sim q) \\ & =\sim p \vee \sim q\end{aligned}\)