The negation of the statement forall x in N, | vedclass

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(D) The given statement is of the form $\forall x \in N, P(x)$,where $P(x)$ is the statement '$x^2+x$ is an even number'.To find the negation of a uni

Vedclass · Accepted Answer

$\exists x \in N$ such that $x^2+x$ is not an even number

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(D) The given statement is of the form $\forall x \in N, P(x)$,where $P(x)$ is the statement '$x^2+x$ is an even number'.To find the negation of a universal quantifier statement $\forall x, P(x)$,we use the rule $\sim(\forall x, P(x)) \equiv \exists x, \sim P(x)$.Here,the negation of '$x^2+x$ is an even number' is '$x^2+x$ is not an even number'.Therefore,the negation of the statement is $\exists x \in N$ such that $x^2+x$ is not an even number.

The negation of the statement $\forall x \in N, x^2+x$ is an even number is

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