The statement pattern $\mathrm{p} \wedge(\mathrm{q} \vee \sim \mathrm{p})$ is equivalent to

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

Solution

$\begin{array}{ll}\mathrm{p} \wedge(\mathrm{q} \vee \sim \mathrm{p}) & \\ \equiv(\mathrm{p} \wedge \mathrm{q}) \vee(\mathrm{p} \wedge \sim \mathrm{p}) & {[\text { Distributive law }]} \\ \equiv(\mathrm{p} \wedge \mathrm{q}) \vee \mathrm{F} & {[\text { complement law }]} \\ \equiv \mathrm{p} \wedge \mathrm{q} & {[\text { Identity law }]}\end{array}$

Asked in: MHT CET 2020 (19 Oct Shift 2)

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