If K₁ = {x : x = n³, n ∈ ℕ}, what type of set is K₁?
Answer and explanation
Correct answer: Infinite set
Taking n = 1, 2, 3, 4, and so on produces K₁ = {1, 8, 27, 64, 125, …}. Natural numbers continue without an ending value, and each distinct natural number gives a distinct cube, so the list of elements never terminates. Therefore K₁ is infinite. It is neither empty nor a singleton, and it is not finite because no final cube exists.
Frequently asked questions
What is the correct answer to this question?
Infinite set
Why is this the correct answer?
Taking n = 1, 2, 3, 4, and so on produces K₁ = {1, 8, 27, 64, 125, …}. Natural numbers continue without an ending value, and each distinct natural number gives a distinct cube, so the list of elements never terminates. Therefore K₁ is infinite. It is neither empty nor a singleton, and it is not finite because no final cube exists.
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.
