Which of the following sets is finite?

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

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

Vedclass · Answer

(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.

Similar Questions

In a group of $50$ people, $35$ speak Hindi, $25$ speak both Hindi and English, and all the people speak Hindi or English or both. The number of people who speak English only is

Let $A = \{a, b, c\}, B = \{b, c, d\}, C = \{a, b, d, e\}$. Then $A \cap (B \cup C)$ is

The domain of the function $f(x) = \log_{3 + x}(x^2 - 1)$ is

In a certain class,$72 \%$ of the students took Biology and $44 \%$ took Mathematics. If each student took at least one of Biology or Mathematics and $40$ students took both of these subjects,the total number of students in the class is:

The equivalent function of $\log {x^2}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module