Determine the truth value of each of these statements if the domain of each variable consists of all real numbers.
- $\forall x \exists y (x^2 = y)$
- $\forall x \exists y ( x= y^2)$
- $\exists x \forall y (xy =0)$
- $\exists x \exists y (x+y \neq y+x)$
- $\forall x (x \neq 0 \rightarrow \exists y (xy=1))$
- $\exists x \forall y (y \neq 0 \rightarrow xy =1) $
- $\forall x \exists y (x+y =1)$
- $\exists x \exists y (x+2y =2 \wedge 2x +4y = 5)$
- $\forall x \exists y (x+y =2 \wedge 2x-y =1)$
- $\forall x \forall y \exists z(z= (x+y)/2)$
