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Which of the following predicate calculus statements is true?

Question 10 options:

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A. ∀n ∈ ℤ, ∃m ∈ ℤ, n = m


B. ∀n ∈ ℤ, ∀m ∈ ℤ, n ≠ m


C. ∀n ∈ ℤ, ∀m ∈ ℤ, n = m


D. ∃n ∈ ℤ, ∀m ∈ ℤ, n ≠ m


Which of the following is the correct predicate calculus translation of the sentence "Some real numbers are not positive"?

Question 11 options:


A. ∃x ∈ ℝ, x < 0


B. ∀x ∈ ℝ, x ≤ 0


C. ∃x ∈ ℝ, x ≤ 0


D. ∀x ∈ ℝ, x < 0


Which of the following counterexamples demonstrates that the following statement of predicate calculus is false "∀n ∈ ℕ, ∃m ∈ ℕ, n = 2m + 1"?

Question 12 options:


A. n = 4


B. m = 4


C. m = 3


D. n = 3

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In the proof shown above, what is the correct justification in the fourth step for the claim that k₁ + k₂ is an integer?

Question 13 options:


A. Definition of odd integers


B. Algebra


C. Definition of even integers


D. Integers are closed under addition


Which of the following is the proper way to begin a proof by contradiction of the theorem "∀p ∀q, p ∈ ℚ ∧ q ∈ ℚ → p + q ∈ ℚ"?

Question 14 options:


A. Suppose the sum of every two irrational numbers is rational


B. Suppose the sum of every two rational numbers is irrational


C. Suppose there exist two rational numbers whose sum is irrational


D. Suppose there exist two irrational numbers whose sum is rational

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Which of the following predicate calculus statements is true? A. n , m , n = m Which of the following is... View the full answer

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