If $\mathrm{p}$ : It is raining. q: Weather is pleasant. then simplified form of the statement "It is not…

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
  1. It is not raining or weather is pleasant
  2. It is raining or weather is not pleasant
  3. It is raining or weather is pleasant
  4. It is raining and the weather is pleasant

Solution

$\mathrm{p}$ : 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.

Asked in: MHT CET 2021 (24 Sep Shift 2)

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