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How can I go about negating predicates? It's asking me to shift a negation in as far inside the predicate as possible.

$$\forall x ((x \ge 100) \lor (x < 100))$$

I am quite new to discrete mathematics so would greatly appreciate a walkthrough. Thanks!

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    $\begingroup$ $ \neg \forall x.P(x) \iff \exists x.\neg P(x)$ $\endgroup$
    – mrp
    Aug 8, 2017 at 12:04

2 Answers 2

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hint

$$\forall \to \;\;\exists $$ $$\ge \to \;\;<$$ $$\lor \to \;\;\land $$

so the negation is

$$\exists x \;: x <100 \;\; \land \;\; x\ge 100$$

remark

Your proposition is always true (tautology), thus its negation is always false (contradiction).

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If you jut want the symbol which represents logical negation, you can visit Wikipedia's symbology page and see that you can use either

$$!$$

Or

$$¬$$

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