Question

Define Infinite set.
Is \[\{ x:x \in R:1 \le x \le 3\} \] an infinite set?
A. True
B. False

Answer 1

Hint: A set is a group of numbers or quantities that can be prescribed or denoted using the brackets, suppose the numbers that a dice consists of are {1, 2, 3, 4, 5, 6} so this is called the set. There are two types of sets, finite and infinite sets. The digits in the above brackets are called the elements of the set. So according to the quantity, we can conclude whether the set is finite and infinite.

Complete step-by-step answer:
Given the set \[\{ x:x \in R:1 \le x \le 3\} \] to find whether it is infinite or not.
Definition of the Infinite set: A set of elements is called the Infinite set when the elements are countless and non-terminating. For example, the stars in the sky are infinite, the water droplets in a lake, the number of natural numbers is infinite and the prime numbers, even numbers, and many more in the Real numbers.
So when we use the set format to define any quantity that is non terminating, then it is called the infinite set.
The given set \[\{ x:x \in R:1 \le x \le 3\} \]can be concluded as an infinite set because the variable x is suggested to be a real number, then there is an infinite number of real numbers between 1 and 3.
Therefore, \[\{ x:x \in R:1 \le x \le 3\} \]is an infinite set. It means the option (A) is correct.
So, the correct answer is “Option A”..

Note: Before answering this question, we have to know what the meaning of the notation R, because the final answer totally depends upon the term R itself. Then we need to find the number of real numbers lies between 1 and 3 to conclude the answer.