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

 1. $\forall x (x^2 \neq x )$
 2. $\exists x \forall y (xy=0)$
 3. $\exists x (x^2= -1)$
 4. $\exists x (x^2+2 > 1)$
 5. $\exists x (x^2 > x)$
 6. $\exists x (x^2=2)$