Which of the following is the negation of the | vedclass

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(C) The given statement is of the form $\forall M > 0, \exists x \in S$ such that $P(x, M)$,where $P(x, M)$ is $x \geqslant M$. To find the negation o

Vedclass · Accepted Answer

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

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(C) The given statement is of the form $\forall M > 0, \exists x \in S$ such that $P(x, M)$,where $P(x, M)$ is $x \geqslant M$. To find the negation of a statement involving quantifiers,we replace $\forall$ with $\exists$ and $\exists$ with $\forall$,and negate the predicate. The negation of $\forall M > 0, \exists x \in S, (x \geqslant M)$ is $\exists M > 0, \forall x \in S, 
eg(x \geqslant M)$. Since the negation of $x \geqslant M$ is $x  0$ such that $x < M$ for all $x \in S$.

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

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