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Question: Answered & Verified by Expert
The negation of the statement $(p \wedge q) \rightarrow(\sim p \vee r)$ is
MathematicsMathematical ReasoningMHT CETMHT CET 2023 (09 May Shift 1)
Options:
  • A $\mathrm{p} \vee \mathrm{q} \vee \sim \mathrm{r}$
  • B $\mathrm{p} \wedge \mathrm{q} \wedge \approx \mathrm{r}$
  • C $\sim p \vee q \wedge r$
  • D $\sim \mathrm{p} \vee \sim \mathrm{q} \vee \sim \mathrm{r}$
Solution:
2324 Upvotes Verified Answer
The correct answer is: $\mathrm{p} \wedge \mathrm{q} \wedge \approx \mathrm{r}$
$\begin{aligned} & \sim[(p \wedge q) \rightarrow(\sim p \vee r)] \\ & \equiv(p \wedge q) \wedge \sim(\sim p \vee r) \ldots[\because \sim(p \rightarrow q) \equiv p \wedge \sim q] \\ & \equiv p \wedge q \wedge p \wedge \sim r \quad \ldots[\text { Associative Law }] \\ & \equiv p \wedge q \wedge \sim r \quad \ldots[\text { Idempotent Law }]\end{aligned}$

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