Solution

The correct answer is A, B, C & E Only.

Key Points

• Statement A: True because for every integer n, there exists an integer m such that n² < m. For example, if n = 2, m can be 5.
• Statement B: True because there exist integers n and m satisfying n + m = 4 and n - m = 2. Solving these equations gives n = 3 and m = 1.
• Statement C: True because integers n and m exist such that n² + m² = 5. For example, n = 1 and m = 2.
• Statement E: True because for every integer m, there exists an integer n such that m + n = 0. For instance, n = -m satisfies this condition.

Additional Information

• Statement D: False because it states that there exists an integer m such that for all integers n, m + n = 0. This is not possible as m + n = 0 cannot hold true for all integers n.
• The universe of discourse consists of all integers, which ensures that the conditions for statements A, B, C, and E are satisfied.