Question

Decide, with justification, on the truth of the following propositions, both when the Universe of discourse is the set of all positive integers, and when the Universe of discourse is the set of all real numbers.

1. ∃x∀y, x < x·y

2. ∀y∃x, x < x·y

3. ∃x∀y, x = x·y

4. ∀y∃x, x = x·y

5. ∀x∃y,∃z, y2 − z2 = 4x

6. ∀x∀y∃z, z < x2 + y2

7. ∀x∃y∃z, x > yz.

Answer 1