Which of the following sets is equal to U = {3, 6, 9, 12}?
Answer and explanation
Correct answer: {x ∈ ℕ : x is a multiple of 3 and x ≤ 12}
A set is equal to U only when it has exactly the same elements. The positive natural multiples of 3 that are less than or equal to 12 are 3, 6, 9, and 12, which gives precisely U. Option A omits 12 because it uses x < 12. Option C omits 3 and 9, while option D includes many nonmultiples of 3. Therefore option B is correct.
Frequently asked questions
What is the correct answer to this question?
{x ∈ ℕ : x is a multiple of 3 and x ≤ 12}
Why is this the correct answer?
A set is equal to U only when it has exactly the same elements. The positive natural multiples of 3 that are less than or equal to 12 are 3, 6, 9, and 12, which gives precisely U. Option A omits 12 because it uses x < 12. Option C omits 3 and 9, while option D includes many nonmultiples of 3. Therefore option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
