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Determine the truth value of each of these statements if the domain of each variable consists of all real numbers.

  1. $\exists x (x^2 = 2)$
  2. $\exists x (x^2= -1)$
  3. $\exists x (x^2+2 >=1)$
  4. $\forall x (x^2 \neq x)$

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