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)

1. AA, B, C Only
2. BB, C, E Only
3. CC, D, E Only
4. DB, D Only

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

Show answer & explanation

Correct answer: A. A, B, C Only

Explanation

A: for any n take m = n² + 1. B: n = −1 is less than every m². C: 1² + 2² = 5. D: no two squares sum to 6. E needs n = 2.5, not an integer. So A, B and C are true.