Which set is infinite but can be written by a simple rule?
Answer and explanation
Correct answer: {x ∈ N : x is a multiple of 3}
The set in option B is {3, 6, 9, 12, ...}. Every positive multiple of 3 belongs to the set, and after any listed multiple another one can be obtained by adding 3. Therefore the set has no last element and is infinite. A simple rule describes how to generate its elements, but it does not make the set finite. Option A is finite, option C has only two elements, and option D is empty under the usual convention N = {1, 2, 3, ...}.
Frequently asked questions
What is the correct answer to this question?
{x ∈ N : x is a multiple of 3}
Why is this the correct answer?
The set in option B is {3, 6, 9, 12, ...}. Every positive multiple of 3 belongs to the set, and after any listed multiple another one can be obtained by adding 3. Therefore the set has no last element and is infinite. A simple rule describes how to generate its elements, but it does not make the set finite. Option A is finite, option C has only two elements, and option D is empty under the usual convention N = {1, 2, 3, ...}.
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.
