If A = {x ∈ ℕ : x ≤ 100}, what is the nature of A?
Answer and explanation
Correct answer: Finite set
Assuming ℕ = {1, 2, 3, ...}, the condition x ≤ 100 gives the elements 1 through 100. Thus A = {1, 2, ..., 100}, which has exactly 100 elements. A set with a fixed, countable number of elements is finite. Therefore option B is correct; the set is not empty or infinite and is certainly not all integers.
Frequently asked questions
What is the correct answer to this question?
Finite set
Why is this the correct answer?
Assuming ℕ = {1, 2, 3, ...}, the condition x ≤ 100 gives the elements 1 through 100. Thus A = {1, 2, ..., 100}, which has exactly 100 elements. A set with a fixed, countable number of elements is finite. Therefore option B is correct; the set is not empty or infinite and is certainly not all integers.
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.
