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

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

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