Pregunta: Let the universe of discourse for each variable be the set of real numbers. Determine if each statement is True ( T ) or False ( F ). 1. ∀x∃y(x+y=1) 2.

Let the universe of discourse for each variable be the set of real numbers. Determine if each statement is True ( T ) or False ( F ).

1. ∀x∃y(x+y=1)

2. ∀x≠0∃y(xy=1)

3. ∃x∀y(xy=0)

4.∃x∃y(x+y≠y+x)

5. ∃x∃y((x+2y=2)∧(2x+4y=5))

6.∀x∀y∃z(z=(x+y/2))

7.∃x(x2=−1)

8. ∀x∃y((x+y=2)∧(2x−y=1))

9. ∃x∀y(xy=1)

10. ∀x∃y(x^2=y)

11.∃x(x^2=2)

12.∀x∃y(x=y^2)