Which of the following is an empty set?

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(A) For option $A$: $x^2+1=0 \Rightarrow x^2=-1$. Since the square of any real number $x \in \mathbb{R}$ is always non-negative $(x^2 \ge 0)$,there is

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$\left\{x: x^2+1=0, x \in \mathbb{R}\right\}$

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(A) For option $A$: $x^2+1=0 \Rightarrow x^2=-1$. Since the square of any real number $x \in \mathbb{R}$ is always non-negative $(x^2 \ge 0)$,there is no real number $x$ that satisfies $x^2=-1$. Thus,the set is empty.For option $B$: $x^2-9=0$ $\Rightarrow x^2=9$ $\Rightarrow x = \pm 3$. This set is $\{3, -3\}$,which is not empty.For option $C$: $x^2-x-2=0$ $\Rightarrow (x-2)(x+1)=0$ $\Rightarrow x=2, -1$. This set is $\{2, -1\}$,which is not empty.For option $D$: $x^2-1=0$ $\Rightarrow x^2=1$ $\Rightarrow x = \pm 1$. This set is $\{1, -1\}$,which is not empty.Therefore,the correct option is $A$.

$(i)$ $\{1, 2, 3, 6\}$	$(a)$ $\{x : x \text{ is a prime number and a divisor of } 6\}$
$(ii)$ $\{2, 3\}$	$(b)$ $\{x : x \text{ is an odd natural number less than } 10\}$
$(iii)$ $\{M, A, T, H, E, I, C, S\}$	$(c)$ $\{x : x \text{ is a natural number and divisor of } 6\}$
$(iv)$ $\{1, 3, 5, 7, 9\}$	$(d)$ $\{x : x \text{ is a letter of the word } MATHEMATICS\}$

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Which of the following is an empty set?

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State whether the following set is finite or infinite:The set of lines which are parallel to the $x$-axis.

Make correct statements by filling in the symbols $\subset$ or $\not\subset$ in the blank spaces:${ x:x \text{ is an even natural number} } \dots { x:x \text{ is an integer} }$

Examine whether the following statement is true or false:$\{x : x \text{ is an even natural number less than } 6\} \subset \{x : x \text{ is a natural number which divides } 36\}$

Which of the following is a set? Justify your answer.The collection of questions in this chapter.