Denial of Universality/Examples

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Examples of Denial of Universality

Example: $\forall x \in S: x \le 3$

Let $S \subseteq \R$ be a subset of the real numbers.

Let $P$ be the statement:

$\forall x \in S: x \le 3$

The negation of $P$ is the statement written in its simplest form as:

$\exists x \in S: x > 3$