Which is the set N = {x : x ∈ ℕ, x ≤ 30, x is a multiple of 6 but not a multiple of 12}?
Answer and explanation
Correct answer: N = {6, 18, 30}
Use the roster-form method by first listing all positive multiples of 6 not exceeding 30: 6, 12, 18, 24, and 30. The phrase “not a multiple of 12” removes 12 and 24, because both are divisible by 12. The remaining numbers, 6, 18, and 30, satisfy every condition in the definition. Thus option A is correct; B forgets the exclusion, while C lists only excluded values.
Frequently asked questions
What is the correct answer to this question?
N = {6, 18, 30}
Why is this the correct answer?
Use the roster-form method by first listing all positive multiples of 6 not exceeding 30: 6, 12, 18, 24, and 30. The phrase “not a multiple of 12” removes 12 and 24, because both are divisible by 12. The remaining numbers, 6, 18, and 30, satisfy every condition in the definition. Thus option A is correct; B forgets the exclusion, while C lists only excluded values.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
