Question
Determine the truth value of each of these statements if the domain of each variable consists of all real numbers.$$\begin{array}{ll}{\text { a) } \quad \exists x\left(x^{2}=2\right)} & {\text { b) } \exists x\left(x^{2}=-1\right)} \\ {\text { c) } \quad \forall x\left(x^{2}+2 \geq 1\right)} & {\text { d) } \forall x\left(x^{2} \neq x\right)}\end{array}$$
Step 1
This statement is saying that there exists a real number x such that when squared, it equals 2. We know that $\sqrt{2}$ and $-\sqrt{2}$ are real numbers and when squared, they equal 2. Therefore, this statement is true. Show more…
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