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Question: Answered & Verified by Expert
If statement $\mathrm{p}$ and $\mathrm{q}$ are true and $\mathrm{r}$ and $\mathrm{s}$ are false, then truth values of $\sim(\mathrm{p} \rightarrow \mathrm{q}) \leftrightarrow(\mathrm{p} \wedge \mathrm{s})$ and $(\sim \mathrm{p} \rightarrow \mathrm{q}) \wedge(\mathrm{r} \leftrightarrow \mathrm{s})$ are respectively.
MathematicsMathematical ReasoningMHT CETMHT CET 2021 (22 Sep Shift 1)
Options:
  • A F, F
  • B T, T
  • C T, F
  • D F, T
Solution:
1639 Upvotes Verified Answer
The correct answer is: T, T
$\begin{aligned} & \sim(\mathrm{p} \rightarrow \mathrm{q}) \leftrightarrow(\mathrm{r} \wedge \mathrm{s}) \\ & \equiv \sim(\mathrm{T} \rightarrow \mathrm{T}) \leftrightarrow(\mathrm{F} \wedge \mathrm{F}) \\ & =\sim(\mathrm{T}) \leftrightarrow \mathrm{F} \equiv \mathrm{F} \leftrightarrow \mathrm{F} \equiv \mathrm{T} \\ & \text { Also }(\sim \mathrm{P} \rightarrow \mathrm{q}) \wedge(\mathrm{r} \leftrightarrow \mathrm{s}) \\ & \equiv(\sim \mathrm{T} \rightarrow \mathrm{T}) \wedge(\mathrm{F} \leftrightarrow \mathrm{F}) \\ & \equiv(\mathrm{F} \rightarrow \mathrm{T}) \wedge(\mathrm{T}) \equiv \mathrm{T} \wedge \mathrm{T} \equiv \mathrm{T}\end{aligned}$

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