Solution to Determine the truth value of each of these statements if the domain of each variable … - Sikademy
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Archangel Macsika

Determine the truth value of each of these statements if the domain of each variable consists of all real numbers. a) ∃x(x2 = −1) b) ∀x(x2 + 2 ≥ 1)

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a) according to statement: for x\in R: \exist x(x^2 = -1). As we know, for \forall x\isin R: x^2 ≥ 0. So, it means, that statement (a) is false.

b) according to statement: for \forall x \isin R:(x^2 + 2 ≥ 1). As we know, for \forall x\isin R: (x^2 ≥ 0)\iff (x^2 + 2 ≥ 2)

That means statement (b) is true.


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