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Question: Answered & Verified by Expert
If $\mathrm{p}$ : It is raining.
q: Weather is pleasant.
then simplified form of the statement "It is not ture, if it is raining then weather is not pleasant" is
MathematicsMathematical ReasoningMHT CETMHT CET 2021 (24 Sep Shift 2)
Options:
  • A It is not raining or weather is pleasant
  • B It is raining or weather is not pleasant
  • C It is raining or weather is pleasant
  • D It is raining and the weather is pleasant
Solution:
1346 Upvotes Verified Answer
The correct answer is: It is raining and the weather is pleasant
$\mathrm{p}$ : it is raining and $\mathrm{q}$ : Weather is pleasant
The symbolic form, of given statement is $\sim(p \rightarrow \sim q)$ $\equiv \sim(\sim \mathrm{p} \vee \sim \mathrm{q})$
$\equiv \mathrm{p} \wedge \mathrm{q}$ i.e. It is raining and the weather is pleasant.

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