Choose the roster form of R = {x : x = 3n, n ∈ ℕ, 2 ≤ n ≤ 6}.
Answer and explanation
Correct answer: R = {6, 9, 12, 15, 18}
The governing concept is substitution in a bounded set-builder rule. Because 2≤n≤6 includes both endpoints, n takes the integer values 2, 3, 4, 5, and 6. Substituting into x=3n gives 6, 9, 12, 15, and 18. The value 3 would require n=1, which is outside the range, while 21 would require n=7. Thus the complete roster is option A.
Frequently asked questions
What is the correct answer to this question?
R = {6, 9, 12, 15, 18}
Why is this the correct answer?
The governing concept is substitution in a bounded set-builder rule. Because 2≤n≤6 includes both endpoints, n takes the integer values 2, 3, 4, 5, and 6. Substituting into x=3n gives 6, 9, 12, 15, and 18. The value 3 would require n=1, which is outside the range, while 21 would require n=7. Thus the complete roster is option A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
