If the universe of discourse is the set of integers, which of the following are TRUE? (A) ∀n∃m (n² < m) (B) ∃n∀m (n < m²) (C) ∃n∀m (nm = m) (D) ∃n∃m (n² + m² = 6) (E) ∃n∃m (n + m = 4 ∧ n − m = 1)
Pick an option to check yourself, or open the answer below.
Show answer & explanation
Correct answer: A. (A), (B) and (C) Only
Explanation
(A) For any n choose m = n² + 1. (B) n = −1 is less than every m². (C) n = 1. (D) No two squares sum to 6. (E) Needs n = 2.5. So (A), (B) and (C) are true.
Note on the official key: the official key says option B. Official/PW key is B ((B) and (C) only). Statement (A) is also true, so option A is correct.
More Discrete Structures and Optimization questions
- Let N² = N × N, where N is the set of natural numbers, and let R be the relation on N² with ⟨x, y⟩ R ⟨u, v⟩ ⇔ xv = yu. Which of the followi…
- Which of the following are tautology? → → → → (A) (P (P Q)) (P Q) → → → ∨ (B) ((P Q) Q) (P Q) ∨¬ → → ∨¬ → (C) ((P P) Q) ((P P) R) → ∧¬ → →…
- Let P(x) be the statement "x = x²". If the universe of discourse is the integers, which of the following are true? (A) P(0) (B) P(1) (C) P(…
- Which of the following statements are true if the universe of discourse is the set of integers? (A) ∀n (n² ≥ 0) (B) ∃n (n² = 2) (C) ∀n (n²…
- Which of the following graphs are trees? (see figure)
- Match List I with List II. List I: (A) ∅ ∩ {∅} = (B) {∅} ∩ {∅} = (C) {∅, {∅}} − ∅ = (D) ∅ ∪ {{∅}} =. List II: (I) ∅ (II) {∅} (III) {{∅}} (I…