If A = {x ∈ Q : 1 < x < 2}, which statement is correct?
Answer and explanation
Correct answer: A is infinite
There are infinitely many rational numbers strictly between 1 and 2. For example, 3/2, 4/3, and 5/4 are distinct members of A. More generally, rational numbers such as (n + 1)/(n) lie between 1 and 2 for every integer n greater than 1, giving infinitely many different elements. Therefore A is infinite, not a singleton or a finite set.
Frequently asked questions
What is the correct answer to this question?
A is infinite
Why is this the correct answer?
There are infinitely many rational numbers strictly between 1 and 2. For example, 3/2, 4/3, and 5/4 are distinct members of A. More generally, rational numbers such as (n + 1)/(n) lie between 1 and 2 for every integer n greater than 1, giving infinitely many different elements. Therefore A is infinite, not a singleton or a finite set.
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.
