If C = {x : x ∈ ℕ, x = 2n, n ∈ ℕ}, what type of set is C?
Answer and explanation
Correct answer: Infinite set
Since x = 2n and n ranges over the natural numbers, C contains even natural numbers such as 2, 4, 6, 8, and so on. There is no greatest natural number, so n can always be increased to produce another even member of C. Consequently, the listing never terminates and C is an infinite set. This conclusion is unchanged whether 0 is included in ℕ.
Frequently asked questions
What is the correct answer to this question?
Infinite set
Why is this the correct answer?
Since x = 2n and n ranges over the natural numbers, C contains even natural numbers such as 2, 4, 6, 8, and so on. There is no greatest natural number, so n can always be increased to produce another even member of C. Consequently, the listing never terminates and C is an infinite set. This conclusion is unchanged whether 0 is included in ℕ.
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.
