Interactive Lecture | Predicates and Quantifiers

Multiple Choice

Which of the following best describes a predicate in logic?

• A statement that includes variables and becomes a proposition when values are substituted for those variables.

• A statement that is always true.

• A mathematical equation with no variables.

• A statement that cannot be evaluated.

Multiple Choice

Given S(x, y): 'x > y+x ', what is the truth vale of S(-1, -1)?

• true

• false

• undefined

Multiple Choice

Given S(x, y): 'x > y+x ', what is the truth value of S(-1, 0)?

• true

• false

• undefined

Multiple Choice

Given R(d, c): 'd is the dean of college c at BPSU', what does the proposition R(Cruz, COEA) represent?

• Cruz is the dean of COEA at BPSU.

• COEA is the dean of Cruz at BPSU.

• Cruz is a student at COEA.

• COEA is a department at BPSU.

Multiple Choice

Which of the following best describes universal quantification?

• It states that a predicate is true for every element under consideration.

• It states that a predicate is true for at least one element under consideration.

• It states that a predicate is true for no elements under consideration.

• It states that a predicate is true for exactly two elements under consideration.

Fill in the Blanks

Fill in the blank: The universal quantification of P(x) is true if P(x) is true for

value(s) of x in the domain.

Open Ended

Explain how the truth value of a universally quantified statement can be determined using an example from the slides.

Multiple Choice

What is a counterexample in the context of universal quantification?

• An element for which the predicate is true.

• An element for which the predicate is false.

• An element that is not in the domain.

• An element that satisfies all predicates.

Multiple Select

Which of the following statements about universal quantification are correct?

• It is true if the predicate is true for every element in the domain.

• It is false if there is at least one element for which the predicate is false.

• It is true if the predicate is true for only one element in the domain.

• It is false if the predicate is true for all but one element in the domain.

Multiple Choice

What does the notation ∃xP(x) represent in the context of quantifiers?

• Universal quantification

• Existential quantification

• Counterexample

• Conjunction

Fill in the Blanks

Fill in the blank: The existential quantification ∃xP(x) is read as 'There is an

such that P(x).'

Multiple Choice

Which of the following is NOT a way to express existential quantification?

• for some

• for at least one

• for every

• there is

Multiple Select

Which of the following statements about the existential quantifier ∃xP(x) are correct?

• It is true if P(x) is true for at least one x in the domain.

• It is false if P(x) is false for every x in the domain.

• It is true if P(x) is true for every x in the domain.

• It is false if P(x) is true for some x in the domain.

Multiple Choice

Let P(x) denote the statement x ≥ 8. What is the truth value of P(5)?

• true

• false

Multiple Choice

What is the truth value of P(-8) if P(x) denotes the statement x ≥ 8?

• true

• false

• undefined

• cannot be determined

Multiple Choice

What is the truth value of P(10) if P(x) denotes the statement x ≥ 8?

• true

• false

• undefined

• cannot be determined

Multiple Choice

What is the truth value of ∃x P(x) if P(x) denotes the statement x ≥ 8?

• true

• false

• undefined

• cannot be determined

Multiple Choice

What is the truth value of ∀x P(x) if P(x) denotes the statement x ≥ 8?

• true

• false

• undefined

• cannot be determined

Multiple Choice

Let P(x) be the statement:  “the word x contains exactly 2 vowels”,
what is the truth value of P(Logic):

• true

• false

• undefined

• cannot be determined

Multiple Choice

Let P(x) be the statement:  “the word x contains exactly 2 vowels”,
what is the truth value of P(Proposition):

• true

• false

• undefined

• cannot be determined

Multiple Choice

Let P(x) be the statement:  “the word x contains exactly 2 vowels”,
what is the truth value of P(Truth):

• true

• false

• undefined

• cannot be determined

Multiple Choice

Let R(x,y) be the statement:  “BPSU College x and Program y it offers”,
what is the truth value of R(COEA, BSCS):

• true

• false

• undefined

• cannot be determined

Multiple Choice

Let R(x,y) be the statement:  “BPSU College x and Program y it offers”,
what is the truth value of R(CCST, BSDS):

• true

• false

• undefined

• cannot be determined

Multiple Choice

Let R(x,y) be the statement:  “BPSU College x and Program y it offers”,
what is the truth value of R(CAHS, BSMid):

• true

• false

• undefined

• cannot be determined

Multiple Choice

Let P(x) be the statement:  “ $$x=x^2$$ ”,,
what is the truth value of P(0):

• true

• false

• undefined

• cannot be determined

Multiple Choice

Let P(x) be the statement:  “ $$x=x^2$$ ”,,
what is the truth value of P(2):

• true

• false

• undefined

• cannot be determined

Multiple Choice

Let P(x) be the statement:  “ $$x=x^2$$ ”,,
what is the truth value of ∀x P(x) :

• true

• false

• undefined

• cannot be determined

Multiple Choice

Let P(x) be the statement:  “ $$x=x^2$$ ”,,
what is the truth value of ∃x P(x) :

• true

• false

• undefined

• cannot be determined

Multiple Choice

Determine if Universal or Existential

For each statement, state whether it uses Universal Quantification (∀) or Existential Quantification (∃).
"There is a file in the folder that is virus-free."

• Universal

• Existential

Multiple Choice

Determine if Universal or Existential

For each statement, state whether it uses Universal Quantification (∀) or Existential Quantification (∃).
"Every programmer knows at least one programming language."

• Universal

• Existential

Multiple Choice

Determine if Universal or Existential

For each statement, state whether it uses Universal Quantification (∀) or Existential Quantification (∃).
"At least one dataset in the repository is biased."

• Universal

• Existential

Multiple Choice

Determine if Universal or Existential

For each statement, state whether it uses Universal Quantification (∀) or Existential Quantification (∃).
"All active users have a verified email address."

• Universal

• Existential

Multiple Choice

Determine if Universal or Existential

For each statement, state whether it uses Universal Quantification (∀) or Existential Quantification (∃).
"There exists a city with 100% renewable energy use."

• Universal

• Existential