The statement pattern $(p \wedge q) \wedge[(p \wedge q) \vee(\sim p \wedge q)]$ is equivalent to

The statement pattern $(p \wedge q) \wedge[(p \wedge q) \vee(\sim p \wedge q)]$ is equivalent to
  1. $q$
  2. $\mathrm{p} \wedge \mathrm{q}$
  3. $p$
  4. $\mathrm{p} \vee \mathrm{q}$

Solution

$\begin{aligned} & (p \wedge q) \wedge[(p \wedge q) \vee(\sim p \wedge q)] \\ & \equiv(p \wedge q) \wedge[q \wedge(p \vee \sim p)] \\ & \equiv(p \wedge q) \wedge[q \wedge T] \equiv(p \wedge q) \wedge q \equiv p \wedge q\end{aligned}$

Asked in: MHT CET 2021 (22 Sep Shift 2)

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