Let m and n be positive integers. Consider:
(A) If n ≠ 1, then m < mn.
(B) If k is composite, then k = mn where 1 < m, n > k.
(C) If mn = 1, then m = 1 and n = 1.
(D) If k is composite, then k = mn where 1 < m, n < k.
Which of the following is correct?
Pick an option to check yourself, or open the answer below.
Show answer & explanation
Correct answer: A. (A), (C), (D)
Explanation
(A): n ≥ 2 so mn ≥ 2m > m, true. (B) is false since factors of k cannot exceed k. (C): the only positive integers with product 1 are 1 and 1, true. (D) is the definition of a composite number, true.More Discrete Structures and Optimisation questions
- Which one of the following is NOT a basic solution of the system of linear equations x₁ + 2x₂ + x₃ = 4 2x₁ + x₂ + 5x₃ = 5
- Match List I with List II: match the logically equivalent propositionsList I List II A. p → q I. (p ∧ q) ∨ (¬p ∧ ¬q) B. ¬(p ∨ (¬p ∧ q)) II.…
- The probability that A hits a target is 1/4, and the probability that B hits the target is 2/5. Both shoot at the target. What is the proba…
- If x and y are elements in a group G and if x⁵ = y³ = e, where e is the identity of G, then the inverse of x²yx⁴y² must be
- Arrange the following graphs on the basis of number of edges in increasing order (for large n): A. Kₙ (Complete Graph) B. Cₙ (Cycle graph)…
- A linear programming problem (LPP) is as follows: Min z = 30x − 18y, subject to the constraints 3x + 4y ≤ 60, 5x − 3y ≥ 20 and x, y ≥ 0. In…