Which of the following sets is finite?

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(A) For option $A$: The equation $x^{2}-2x-3=0$ can be factored as $(x-3)(x+1)=0$. Thus,$x=3$ or $x=-1$. Since both $3$ and $-1$ are integers,the set

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$A = \{x : x \in Z 	ext{ and } x^{2}-2x-3=0\}$

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(A) For option $A$: The equation $x^{2}-2x-3=0$ can be factored as $(x-3)(x+1)=0$. Thus,$x=3$ or $x=-1$. Since both $3$ and $-1$ are integers,the set $A = \{3, -1\}$. This set contains a finite number of elements,so it is a finite set.For option $B$: The set of natural numbers divisible by $2$ is ${2, 4, 6, 8, 10, \dots}$. This set continues indefinitely,so it is an infinite set.For option $C$: An infinite number of lines can pass through a single point in a plane. Therefore,$C$ is an infinite set.For option $D$: The set of integers $x > -5$ is $\{-4, -3, -2, -1, 0, 1, 2, \dots\}$. This set continues indefinitely,so it is an infinite set.Conclusion: Only set $A$ is finite.

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