Determine the truth value of the following statements if the universe of discourse of each variable is the set of real numbers.

 1. $\forall x \exists y (x=y^2)$
 2. $\forall x \neq 0 \exists y (xy=1)$
 3. $\forall x \exists y (x^2=y)$
 4. $\forall x \exists y ((x+y=2) \land (2x-y=1))$
 5. $\exists x \forall y (xy=0)$
 6. $\exists x (x^2=2)$
 7. $\exists x \exists y (x + y \neq y + x)$
 8. $\forall x \forall y \exists z (z = \frac{x+y}{2})$
 9. $\exists x (x^2= -1)$
 10. $\forall x \exists y (x+y=1)$
 11. $\exists x \exists y ((x+2y=2) \land (2x+4y=5))$
 12. $\exists x \forall y \neq 0 (xy=1)$