Q69 / 150 · MHT CET 2020 (14 Oct Shift 1) · Mathematics

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

  • A
    $\mathrm{q}$
  • B
    $\sim q$
  • C
    $\sim \mathrm{p}$
  • Correct answer
    D
    $\mathrm{p}$

Solution

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

Hence, the correct answer is option: 'D'.

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