Unit 1 · Discrete Structures and Optimisation Paper 2 CS · June 2024 (Cancelled Exam)

Which of the following are TRUE if the universe of discourse consists of all integers?
A. ∀n ∃m (n² < m)
B. ∃n ∀m (n < m²)
C. ∃n ∃m (n² + m² = 5)
D. ∃n ∃m (n² + m² = 6)
E. ∃n ∃m (m + n = 4 ∧ n − m = 1)
Choose the correct answer from the options given below:

Pick an option to check yourself, or open the answer below.

Show answer & explanation

Correct answer: A. A, B, C Only

Explanation

A: take m = n² + 1. B: n = −1. C: 1² + 2² = 5. D has no integer solution, and E forces n = 2.5.