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

University of Michigan - Ann Arbor

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

University of Michigan EECS 203 Lecture Notes

$$\forall$$: "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)

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