MATH 170 A Quiz

Which of the following represents the set {x ∈ ℝ | x < 1 or x ≥ 4}?

• ℝ ∩ (1,4)

• ℝ ∩ [1,4)

• ℝ - [1,4]

• ℝ - (1,4)

Let X = {1,2,3,4,5,6,7,8} and Y = {1,6,7,8}. Which of the following represents the set X - Y?

• ℕ - [2, 5]

• ℕ - (2, 5)

• ℕ ∩ (2, 5)

• ℕ ∪ (2,5)

Find the truth values of p and q that will make the statement p ↔ (p̃ ∧ q) true.

• 𝑝 = True , 𝑞 = True

• 𝑝 = True , 𝑞 = False

• 𝑝 = False , 𝑞 = True

• 𝑝 = False , 𝑞 = False

• t’s not possible for the statement to be true

What truth values of p and q would prove that propositions M and V are not logically equivalent? M: (p̃ ∧ q) → (p ∨ q) V: p ∨ q̃

• 𝑝 = True , 𝑞 = True

• 𝑝 = True , 𝑞 = False

• 𝑝 = False , 𝑞 = True

• 𝑝 = False , 𝑞 = False

Find the truth value of these two statements if p is True and q is False: Statement #1: ¬p ∨ q Statement #2: (p ∧ q) → (p ∨ q)

• both statements are true

• both statements are false

• statement #1 is true, statement #2 is false

• statement #1 is false, statement #2 is true

Let X be a subset of Y. Find the truth value of these two statements: Statement #1: X ∪ Y = Y Statement #2: X – Y = Ø

• both statements are true

• both statements are false

• statement #1 is true, statement #2 is false

• statement #1 is false, statement #2 is true

Find the truth value of these two statements: Statement #1: (2,3) ∈ [1,4] Statement #2: [2,3] ∩ [3,8] = Ø

• both statements are true

• both statements are false

• statement #1 is true, statement #2 is false

• statement #1 is false, statement #2 is true

Find the truth value of these two statements: Statement #1: ∀x ∈ Z(x² ≥ x) Statement #2: ∃x ∈ ℝ⁺(x – 2 < 0)

• both statements are true

• both statements are false

• statement #1 is true, statement #2 is false

• statement #1 is false, statement #2 is true

Find the truth value of these two statements: Statement #1: ∀x ∈ ℝ(x^3 > 0) Statement #2: ∃x ∈ ℤ(x^2 - 2 = 0)

• both statements are true

• both statements are false

• statement #1 is true, statement #2 is false

• statement #1 is false, statement #2 is true

Which of the following represents the set Z ∩ [-2, 3]?