MHT CET · Maths · Mathematical Reasoning
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
- 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
Answer & Solution
Correct Answer
(D) It is raining and the weather is pleasant
Step-by-step Solution
Detailed explanation
\(\mathrm{p}\) : 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.
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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