If A = {x : x is a multiple of 3, x ≤ 15} and B = {x : x is a multiple of 5, x ≤ 15}, what is A ∪ B?
Answer and explanation
Correct answer: {3, 5, 6, 9, 10, 12, 15}
The multiples of 3 not exceeding 15 are A = {3, 6, 9, 12, 15}, while the multiples of 5 not exceeding 15 are B = {5, 10, 15}. The union contains every element that belongs to A or B, but repeated elements are written only once. Therefore, A ∪ B = {3, 5, 6, 9, 10, 12, 15}. The common element 15 is included only once.
Frequently asked questions
What is the correct answer to this question?
{3, 5, 6, 9, 10, 12, 15}
Why is this the correct answer?
The multiples of 3 not exceeding 15 are A = {3, 6, 9, 12, 15}, while the multiples of 5 not exceeding 15 are B = {5, 10, 15}. The union contains every element that belongs to A or B, but repeated elements are written only once. Therefore, A ∪ B = {3, 5, 6, 9, 10, 12, 15}. The common element 15 is included only once.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
