Which statement is correct about A = {x ∈ Q : 0 < x < 1}?
Answer and explanation
Correct answer: It is an infinite set
There are infinitely many rational numbers strictly between 0 and 1. For example, 1/2, 1/3, and 2/3 belong to A, and for every positive integer n, the rational number 1/(n + 1) also lies between 0 and 1. Thus new distinct elements can be generated endlessly. The endpoints 0 and 1 are excluded, but excluding them does not make the set finite.
Frequently asked questions
What is the correct answer to this question?
It is an infinite set
Why is this the correct answer?
There are infinitely many rational numbers strictly between 0 and 1. For example, 1/2, 1/3, and 2/3 belong to A, and for every positive integer n, the rational number 1/(n + 1) also lies between 0 and 1. Thus new distinct elements can be generated endlessly. The endpoints 0 and 1 are excluded, but excluding them does not make the set finite.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
