The logical expression $[p \wedge(q \vee r)] \vee[\sim r \wedge \sim q \wedge p]$ is equivalent to

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

Solution

$[p \wedge(q \vee r)] \vee[\sim r \wedge \sim \wedge \wedge p]$ $\equiv[p \wedge(q \vee r)] \vee[p \wedge(\sim q \wedge \sim r)]$ $\underline{\underline{\underline{\alpha}}}[p \wedge(q \vee r)] \vee[p \wedge(\sim(q \vee r))]$ $=p \wedge[(q \vee r) \vee(\sim(q \vee r))]$ $=p \wedge T=p$

Asked in: MHT CET 2020 (14 Oct Shift 1)

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