If p: It rains today,q: I go to school,r: I s | vedclass

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Question

(A) Given propositions are:$p$: It rains today$q$: $I$ go to school$r$: $I$ shall meet my friend$s$: $I$ shall go for a movieThe statement is: "If it

Vedclass · Accepted Answer

$\sim (p \wedge q) \Rightarrow (r \wedge s)$

Vedclass · Answer

(A) Given propositions are:$p$: It rains today$q$: $I$ go to school$r$: $I$ shall meet my friend$s$: $I$ shall go for a movieThe statement is: "If it does not rain or if $I$ do not go to school,then $I$ shall meet my friend and go for a movie.""It does not rain" is $\sim p$."$I$ do not go to school" is $\sim q$."It does not rain or if $I$ do not go to school" is $(\sim p \vee \sim q)$.By De Morgan's Law,$(\sim p \vee \sim q) \equiv \sim (p \wedge q)$."$I$ shall meet my friend and go for a movie" is $(r \wedge s)$.Thus,the proposition is $\sim (p \wedge q) \Rightarrow (r \wedge s)$.Therefore,the correct option is $A$.

If $p$: It rains today,$q$: $I$ go to school,$r$: $I$ shall meet my friend,and $s$: $I$ shall go for a movie,then which of the following represents the proposition: "If it does not rain or if $I$ do not go to school,then $I$ shall meet my friend and go for a movie"?

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