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Question: Answered & Verified by Expert
The logical expression
$[\mathrm{p} \wedge(\mathrm{q} \vee \mathrm{r})] \vee[(\sim \mathrm{p} \wedge \mathrm{q}) \vee(\sim \mathrm{p} \wedge \mathrm{r})]$ is equivalent to
MathematicsMathematical ReasoningMHT CETMHT CET 2020 (20 Oct Shift 2)
Options:
  • A $\mathrm{p}$
  • B $\mathrm{q}$
  • C $\mathrm{p} \wedge \mathrm{r}$
  • D $\mathrm{q} \vee \mathrm{r}$
Solution:
1054 Upvotes Verified Answer
The correct answer is: $\mathrm{q} \vee \mathrm{r}$
$[p \wedge(q \vee r)] \vee[(\sim p \wedge q) \vee(\sim p \wedge r)]$
$\equiv[p \wedge(q \vee r)] \vee[\sim p \wedge(q \vee r)]$
$\equiv(q \vee r) \wedge(p \vee \sim p)$
$\equiv(q \vee r) \wedge T$
$\equiv q \vee r$

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