If A = {x ∈ ℕ : 100 < x < 999}, what type of set is A?
Answer and explanation
Correct answer: Finite set
The natural numbers satisfying 100 < x < 999 are 101, 102, 103, ..., 998. This is a bounded list of consecutive natural numbers, so it contains only finitely many elements. In fact, its cardinality is 998 − 101 + 1 = 898. The strict inequalities exclude 100 and 999, but they do not make the set empty or infinite.
Frequently asked questions
What is the correct answer to this question?
Finite set
Why is this the correct answer?
The natural numbers satisfying 100 < x < 999 are 101, 102, 103, ..., 998. This is a bounded list of consecutive natural numbers, so it contains only finitely many elements. In fact, its cardinality is 998 − 101 + 1 = 898. The strict inequalities exclude 100 and 999, but they do not make the set empty or infinite.
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.
