If A = {x : x ∈ N, x is a two-digit number}, what type of set is A?
Answer and explanation
Correct answer: Finite set
The two-digit natural numbers are 10, 11, 12, ..., 99. This collection has a definite first element and a definite last element, so its members can be counted completely. In fact, it contains 99 − 10 + 1 = 90 elements. Therefore, A is a finite set, even though it has many elements. It is neither empty, nor infinite, nor a singleton.
Frequently asked questions
What is the correct answer to this question?
Finite set
Why is this the correct answer?
The two-digit natural numbers are 10, 11, 12, ..., 99. This collection has a definite first element and a definite last element, so its members can be counted completely. In fact, it contains 99 − 10 + 1 = 90 elements. Therefore, A is a finite set, even though it has many elements. It is neither empty, nor infinite, nor a singleton.
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.
