If C = {x : x ∈ ℕ, 2x + 3 ≤ 15}, what is the correct roster form of C?
Answer and explanation
Correct answer: C = {1, 2, 3, 4, 5, 6}
Solve the inequality: 2x + 3 ≤ 15 gives 2x ≤ 12, and hence x ≤ 6. Under the convention used here, ℕ denotes the positive natural numbers 1, 2, 3, and so on. Therefore, the natural numbers satisfying x ≤ 6 are 1, 2, 3, 4, 5 and 6. Thus the roster form is option A. Option B incorrectly includes zero, while C omits 6.
Frequently asked questions
What is the correct answer to this question?
C = {1, 2, 3, 4, 5, 6}
Why is this the correct answer?
Solve the inequality: 2x + 3 ≤ 15 gives 2x ≤ 12, and hence x ≤ 6. Under the convention used here, ℕ denotes the positive natural numbers 1, 2, 3, and so on. Therefore, the natural numbers satisfying x ≤ 6 are 1, 2, 3, 4, 5 and 6. Thus the roster form is option A. Option B incorrectly includes zero, while C omits 6.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
