In mathematics, an example for a proposition with a universal quantifier $\big({\forall}_{x \in X} \; P(x)\big)$ or an existential quantifier $\big(\underset{x \in X}{\exists}\; P(x) \big)$ is a term $x$ of type $X$ for which $P(x)$ is true (inhabited).
Every counterexample is an example of the negation of a proposition.
mathematical statements
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