If J = {x : x = 3n + 1, n ∈ N}, where N = {1, 2, 3, ...}, what type of set is J?
Answer and explanation
Correct answer: Infinite set
Since n can be any positive natural number, substituting n = 1, 2, 3, 4, ... gives J = {4, 7, 10, 13, ...}. There is no greatest permitted value of n, so new elements continue to appear without end. The set therefore has infinitely many elements and is an infinite set, not a finite or singleton set.
Frequently asked questions
What is the correct answer to this question?
Infinite set
Why is this the correct answer?
Since n can be any positive natural number, substituting n = 1, 2, 3, 4, ... gives J = {4, 7, 10, 13, ...}. There is no greatest permitted value of n, so new elements continue to appear without end. The set therefore has infinitely many elements and is an infinite set, not a finite or singleton set.
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.
