If p : It is raining today.q : I go to school | vedclass

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Question

(D) Given statements:$p :$ It is raining today.$q :$ $I$ go to school.$r :$ $I$ will meet my friends.$s :$ $I$ will go to watch a movie.Negations:$\si

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) Given statements:$p :$ It is raining today.$q :$ $I$ go to school.$r :$ $I$ will meet my friends.$s :$ $I$ will go to watch a movie.Negations:$\sim p :$ It does not rain today.$\sim q :$ $I$ do not go to school.The statement is: 'If it does not rain today or $I$ do not go to school,then $I$ will meet my friends and go to watch a movie'.This can be written as: $(\sim p \vee \sim q) \Rightarrow (r \wedge s)$.Since $(\sim p \vee \sim q)$ is equivalent to $\sim (p \wedge q)$ by De Morgan's Law,the statement can also be represented as $\sim (p \wedge q) \Rightarrow (r \wedge s)$.

If $p :$ It is raining today.
$q :$ $I$ go to school.
$r :$ $I$ will meet my friends.
$s :$ $I$ will go to watch a movie.
Then write the statement: 'If it does not rain today or $I$ do not go to school,then $I$ will meet my friends and go to watch a movie' in symbolic form.

Similar Questions

Which of the following statements is logically equivalent to $\sim (p \leftrightarrow q)$?

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Let $p, q, r$ be three statements such that the truth value of $(p \wedge q) \rightarrow (\sim q \vee r)$ is $F$. Then the truth values of $p, q, r$ are respectively:

The negation of the converse of the statement $p \lor q$ is:

If $\sim p \vee q$ is false, then which of the following is correct?

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If $p :$ It is raining today.$q :$ $I$ go to school.$r :$ $I$ will meet my friends.$s :$ $I$ will go to watch a movie.Then write the statement: 'If it does not rain today or $I$ do not go to school,then $I$ will meet my friends and go to watch a movie' in symbolic form.