$$\forall$$: "for all", "every", "any"
- all includes the universe of discourse or domain of discourse

"everyone will buy an umbrella"
- $$\forall$$ x B(x, umbrella)

Universal quantifier

 $$\exists$$ : "there exists", "at least one", "some"

"someone will buy an umbrella"
$$\exists$$ x B(x, umbrella)

Existential qualifier

Two statements with quantifiers and predicates are logically equivalent if they have the same truth table regardless of the meaning of the predicates and the domain of discourse

Equivalence with quantifiers

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"

University of Michigan - Ann Arbor

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.

Predicates

University of Michigan EECS 203 Lecture Notes

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)

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