Explicitly defines objects and relations among those objects. For example take the following sentence:
- "Dan is taller than both his mothers, but they’re the same height.”

The objects: 
- Dan
- M1 = Mother 1
- M2 = Mother 2

The relations:
- T(x, y) = "x is taller than y"

The predicate:
- T(Dan, M1) $$\land$$ T(Dan, M2) $$\land$$ $$\lnot$$ T(M1, M2) $$\land$$ $$\lnot$$ T(M2, M1)

Predicate logic

How to refer to someone or everyone (at least one or all)...

Universal quantifier ($$\forall$$)
- "for all", "every", "any"

Existential quantifier ($$\exists$$)
- "there exists", "at least one", "some"

Predicates and quantification

A declarative statement with some terms left unspecified. A predicate can become a proposition when the terms are specified. These terms are referred to as objects.

University of Michigan - Ann Arbor

Basic concepts in Discrete math

A declarative statement that is either true or false

Propositions (mathematics)

an inferential argument for a mathematical statement that uses assumptions to logically show the conclusion is valid

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