Week 5 Logic of Quantified statments

what is a predicate?

A predicate (or propositional function) is a statement containing one or more variables. If values from a given set (domain) are assigned to all the variables, the resulting statement is a proposition.

what are quantifies?

words that refer to quantities such as "some" or "all"

what is the symbol for Universal quantifier?

∀

Explain universla quantifier

The symbol ∀ (an upside-down A) is called the universal quantifer; the meaning is for all (for each)

What is the symbol for Existential quantifier

∃

explain Existential quantifier

there exists

Write in shorthand the following: For a predicate p(x) with domain D the statement "for every x from domain D, p(x)"

∀x ∈ D p(x)

Write in shorthand the following: For a predicate p(x) with domain D the statement "there exists an x from the domain D such that p(x)"

∃x ∈ D, p(x)