Logic II

Question 1

predicate

Answer 1

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

Question 2

domain in a predicate

Answer 2

set of all possible values for the variable

Question 3

difference between predicate and proposition

Answer 3

predicates can have variables, propositions cannot

Question 4

universal quantifier (∀)

Answer 4

true for every possible value for x in its domain

Question 5

universally quantified statement (∀x P(x))

Answer 5

a proposition

Question 6

arbitrary element

Answer 6

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

Question 7

counterexample

Answer 7

an element in the domain for which the predicate is false

Question 8

existential quantifier (∃)

Answer 8

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

Question 9

existentially quantified statement (∃x P(x))

Answer 9

a proposition

Question 10

quantifiers

Answer 10

general term for universal and existential quantifiers

Question 11

quantified statement

Answer 11

logical statement that includes a universal or existential quantifier

Question 12

when are quantifiers applied?

Answer 12

before the logical operations used for propositions

∀x P(x) ∧ Q(x) == (∀x P(x)) ∧ Q(x)

Question 13

free variable

Answer 13

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

Question 14

bound variable

Answer 14

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

Question 15

is (∀x P(x)) ∧ Q(x) a proposition?

Answer 15

no, x is both bound and free

Question 16

is ∀x (P(x) ∧ Q(x)) a proposition?

Answer 16

yes, x is bound

Question 17

¬∀x F(x) is logically equivalent to

Answer 17

∃x ¬F(x)