If K = {x : x = 3n + 1, n ∈ N, n ≤ 5}, where N = {1, 2, 3, ...}, what type of set is K?
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Answer and explanation
Correct answer: Finite set
Because n is a natural number and n ≤ 5, its possible values are only 1, 2, 3, 4, and 5. The corresponding values of x = 3n + 1 are 4, 7, 10, 13, and 16. Thus K = {4, 7, 10, 13, 16}, which has five elements and is therefore finite. The upper bound on n is decisive.
Frequently asked questions
What is the correct answer to this question?
Finite set
Why is this the correct answer?
Because n is a natural number and n ≤ 5, its possible values are only 1, 2, 3, 4, and 5. The corresponding values of x = 3n + 1 are 4, 7, 10, 13, and 16. Thus K = {4, 7, 10, 13, 16}, which has five elements and is therefore finite. The upper bound on n is decisive.
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.
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