The negation of the statement "If an integer | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $p$ be the statement "An integer is greater than $4$ and less than $5$" and $q$ be the statement "It is a multiple of $3$".The given statement

Vedclass · Accepted Answer

An integer is greater than $4$ and less than $5$ and it is not a multiple of $3$.

Vedclass · Answer

(A) Let $p$ be the statement "An integer is greater than $4$ and less than $5$" and $q$ be the statement "It is a multiple of $3$".The given statement is in the form "If $p$, then $q$", which is denoted as $p \implies q$.The negation of $p \implies q$ is $\sim(p \implies q) \equiv p \land \sim q$.Here, $p \land \sim q$ means "An integer is greater than $4$ and less than $5$ and it is not a multiple of $3$".Comparing this with the given options, option $(A)$ and $(D)$ represent the same logical statement. Since option $(A)$ is the standard form, it is the correct choice.

The negation of the statement "If an integer is greater than $4$ and less than $5$, then it is a multiple of $3$" is:

Similar Questions

Consider the two statements:
$(S1): (p$ $\rightarrow q) \vee (\sim q$ $\rightarrow p)$ is a tautology.
$(S2): (p \wedge \sim q) \wedge (\sim p \vee q)$ is a fallacy.
Then:

If the truth value of $[(p \lor q) \land (q \to r) \land (\sim r)] \to (p \land q)$ is false, then which of the following is $NOT$ true?

The statement pattern $(p \wedge q) \wedge [\sim r \vee (p \wedge q)] \vee (\sim p \wedge q)$ is equivalent to $......$

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

The statement pattern $p \rightarrow \sim(p \wedge \sim q)$ is equivalent to

Vedclass Test Series

Exam Paper Generator

Online Exam Module