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Flashcards in Logic II Deck (17)
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1

predicate

logical statement whose truth value is a function of one or more variables

2

domain in a predicate

set of all possible values for the variable

3

difference between predicate and proposition

predicates can have variables, propositions cannot

4

universal quantifier (∀)

true for every possible value for x in its domain

5

universally quantified statement (∀x P(x))

a proposition

6

arbitrary element

means nothing is assumed about the element other than the fact that it is in the domain

7

counterexample

an element in the domain for which the predicate is false

8

existential quantifier (∃)

true for at least one possible value for x in its domain

9

existentially quantified statement (∃x P(x))

a proposition

10

quantifiers

general term for universal and existential quantifiers

11

quantified statement

logical statement that includes a universal or existential quantifier

12

when are quantifiers applied?

before the logical operations used for propositions
∀x P(x) ∧ Q(x) == (∀x P(x)) ∧ Q(x)

13

free variable

a variable x in the predicate P(x), because variable is free to take on any value in the domain

14

bound variable

variable x in the statement ∀x P(x), because the variable is bound to a quantifier

15

is (∀x P(x)) ∧ Q(x) a proposition?

no, x is both bound and free

16

is ∀x (P(x) ∧ Q(x)) a proposition?

yes, x is bound

17

¬∀x F(x) is logically equivalent to

∃x ¬F(x)