How can the set B = {2, 5, 10, 17, 26} be written most accurately in set-builder form?
Answer and explanation
Correct answer: B = {x : x = n² + 1, n ∈ N, 1 ≤ n ≤ 5}
For n = 1, 2, 3, 4, and 5, the expression n² + 1 gives 2, 5, 10, 17, and 26 respectively. Therefore, the rule generating every element is x = n² + 1. The restriction 1 ≤ n ≤ 5 is essential because it produces exactly the five listed elements; without this restriction, option D would generate infinitely many additional values.
Frequently asked questions
What is the correct answer to this question?
B = {x : x = n² + 1, n ∈ N, 1 ≤ n ≤ 5}
Why is this the correct answer?
For n = 1, 2, 3, 4, and 5, the expression n² + 1 gives 2, 5, 10, 17, and 26 respectively. Therefore, the rule generating every element is x = n² + 1. The restriction 1 ≤ n ≤ 5 is essential because it produces exactly the five listed elements; without this restriction, option D would generate infinitely many additional values.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
