Which of the following is the empty set?

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(B) The empty set is a set that contains no elements.For option $A$: $x^2 - 1 = 0$ $\Rightarrow x^2 = 1$ $\Rightarrow x = \pm 1$. These are real numbe

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$ \{ x : x 	ext{ is a real number and } x^2 + 1 = 0 \} $

Vedclass · Answer

(B) The empty set is a set that contains no elements.For option $A$: $x^2 - 1 = 0$ $\Rightarrow x^2 = 1$ $\Rightarrow x = \pm 1$. These are real numbers,so the set is $\{ -1, 1 \}$.For option $B$: $x^2 + 1 = 0 \Rightarrow x^2 = -1$. There is no real number $x$ such that its square is negative. Thus,this set is empty.For option $C$: $x^2 - 9 = 0$ $\Rightarrow x^2 = 9$ $\Rightarrow x = \pm 3$. These are real numbers,so the set is $\{ -3, 3 \}$.For option $D$: $x^2 - x - 2 = 0$ $\Rightarrow (x - 2)(x + 1) = 0$ $\Rightarrow x = 2, -1$. These are real numbers,so the set is $\{ -1, 2 \}$.Therefore,the correct option is $B$.

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