Predicate Logic

Question 1

predicate

Answer 1

A proposition whose truth value depends on the truth value of one or more variables of a propositional function(s)

Question 2

universe of discourse

Answer 2

A set that contains the possible values of the variable(s) in the predicate.

Question 3

quantifier

Answer 3

Symbols used to indicate the “scope” of the predicate.

Question 4

universal quantification

Answer 4

The universal quantification of a predicate (say, P(x)) is the proposition “P(x) is true for ALL values of x in some set D.”

Question 5

universal quantifier symbol

Answer 5

∀

Question 6

existential quantification

Answer 6

The existential quantification of a predicate (say, P(x)) is the proposition “There exists an element 𝑥 in some set D such that P(𝑥) is true.”

Question 7

existential quantifier symbol

Answer 7

∃

Question 8

Words used for universal quantification

Answer 8

“For every”, “All”, “Everything”, “Everyone”

Question 9

Words used for existential quantification

Answer 9

“There exists some/an”, “An”, “At least one”, “some”, “one or more”

Question 10

¬(∀x ∈ 𝐷 𝑃 x )

Answer 10

∃x ∈ 𝐷 ¬𝑃(x)

Question 11

¬(∃x ∈ 𝐷 𝑃(x))

Answer 11

∀x ∈ 𝐷 ¬𝑃(x)