If p: It is raining. q: Weather is pleasant. | vedclass

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Question

(D) Let $p$: It is raining and $q$: The weather is pleasant. The given statement is "It is not true that,if it is raining then the weather is not plea

Vedclass · Accepted Answer

It is raining and the weather is pleasant

Vedclass · Answer

(D) Let $p$: It is raining and $q$: The weather is pleasant. The given statement is "It is not true that,if it is raining then the weather is not pleasant". Symbolically,this is written as $\sim(p \rightarrow \sim q)$. Using the logical equivalence $\sim(A \rightarrow B) \equiv A \wedge \sim B$,we get: $\sim(p \rightarrow \sim q) \equiv p \wedge \sim(\sim q)$. Since $\sim(\sim q) \equiv q$,the expression simplifies to $p \wedge q$. Thus,the statement is "It is raining and the weather is pleasant".

If $p$: It is raining. $q$: Weather is pleasant. Then the simplified form of the statement "It is not true that,if it is raining then the weather is not pleasant" is

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