Which of the following is the negation of the | vedclass

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(C) Let the statement $P$ be: "For all $M > 0$,there exists $x \in S$ such that $x \geq M$." The negation of a statement involving quantifiers follows

Vedclass · Accepted Answer

there exists $M > 0$,such that $x < M$ for all $x \in S$

Vedclass · Answer

(C) Let the statement $P$ be: "For all $M > 0$,there exists $x \in S$ such that $x \geq M$." The negation of a statement involving quantifiers follows these rules: $1$. The negation of "for all" $(\forall)$ is "there exists" $(\exists)$. $2$. The negation of "there exists" $(\exists)$ is "for all" $(\forall)$. $3$. The negation of $x \geq M$ is $x Applying these rules to $P$: $\sim P$: "There exists $M > 0$ such that for all $x \in S$,$x Thus,the correct option is $C$.

Which of the following is the negation of the statement "for all $M > 0$,there exists $x \in S$ such that $x \geq M$"?

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