The negation of forall n in N, n+7 6 is ... | vedclass

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

Question

(A) Key Idea: The negation of the universal quantifier $\forall$ (for all) is the existential quantifier $\exists$ (there exists),and the negation of

Vedclass · Accepted Answer

$\exists n \in N$,such that $n+7 \leq 6$

Vedclass · Answer

(A) Key Idea: The negation of the universal quantifier $\forall$ (for all) is the existential quantifier $\exists$ (there exists),and the negation of the inequality $>$ is $\leq$. Given the statement: $\forall n \in N, n+7 > 6$. Applying the rules of negation: $1$. Replace $\forall$ with $\exists$. $2$. Negate the condition $n+7 > 6$,which becomes $n+7 \leq 6$. Therefore,the negation of the given statement is $\exists n \in N$,such that $n+7 \leq 6$.

The negation of $\forall n \in N, n+7 > 6$ is ....

Similar Questions

Which of the following is not a statement?

If $(p \wedge \sim q) \wedge (p \wedge r) \rightarrow \sim p \vee q$ is false,then the truth values of $p, q$ and $r$ are respectively

By giving a counterexample,show that the following statement is not true.
$q:$ The equation $x^{2}-1=0$ does not have a root lying between $0$ and $2$.

Write the following statement in the form "if-then":
$A$ quadrilateral is a parallelogram if its diagonals bisect each other.

$p \Rightarrow q$ can also be written as

Vedclass Test Series

Exam Paper Generator

Online Exam Module