How can the set B = {0, 3, 8, 15, 24} be correctly written in set-builder form?
Answer and explanation
Correct answer: B = {x : x = n² − 1, n ∈ ℕ, 1 ≤ n ≤ 5}
Examine the elements using their positions. For n = 1, 2, 3, 4, 5, the expression n² − 1 gives 0, 3, 8, 15, and 24 respectively. Thus every listed element is generated by x = n² − 1, and the restriction 1 ≤ n ≤ 5 produces exactly the five members of B. The other expressions generate different numbers, so option A is correct.
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?
Examine the elements using their positions. For n = 1, 2, 3, 4, 5, the expression n² − 1 gives 0, 3, 8, 15, and 24 respectively. Thus every listed element is generated by x = n² − 1, and the restriction 1 ≤ n ≤ 5 produces exactly the five members of B. The other expressions generate different numbers, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
