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 numbers,s

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

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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 numbers,so the set is $\{1, -1\}$.For option $B$: $x^2 + 1 = 0 \Rightarrow x^2 = -1$. There is no real number whose square is $-1$. Thus,this set contains no elements and is the empty set.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 $\{2, -1\}$.Therefore,the correct option is $B$.

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