Predicate logic

Predicate logic is the logic we are currently using

Logical symbols
Logical symbols vary by author, but usually include the following:
 * Quantifier symbols: ∀ for universal quantification, and ∃ for existential quantification
 * Logical connectives: ∧ for conjunction, ∨ for disjunction, → for implication, ↔ for biconditional, ¬ for negation.
 * Parentheses, brackets, and other punctuation symbols. The choice of such symbols varies depending on context.

Predicates example
(∀x∃y∀z)P(x, y, z)

For all people, there is a kind of food, such that they like all instances of that kind of food

If you mess up the order of the existential quantifiers you can get a completely different sentence

(∃y∀x∀z)P(x, y, z)

There exists a kind of food, for which all people like all instances of that kind of food

Totally different

Non examples
(∀x)[P(x) | P=Q(x)] → [(∀x)P(x)] | [(∀x)P=Q(x)]

All numbers are either even or odd → All numbers are odd, or all numbers are even\