How to negate predicates?

Question

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!

Answer 1

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).

Answer 2

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

$$¬$$