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

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

Solution

$\sim(p \vee q) \vee(\sim p \wedge q)$ $=(\sim p \wedge \sim q) \vee(\sim p \wedge q)$ $\equiv \sim p \wedge(\sim q \vee q)$ $\equiv \sim p \wedge T \cong \sim p$

Asked in: MHT CET 2020 (13 Oct Shift 2)

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