If A = {2, 4, 6, 8, 10, 12}, B = {3, 6, 9, 12, 15}, and C = {6, 12, 18}, what is (A ∪ B) ∩ C?
Answer and explanation
Correct answer: {6, 12}
First form the union A ∪ B by listing every element that occurs in either A or B, without repeating any element. This gives {2, 3, 4, 6, 8, 9, 10, 12, 15}. Now intersect this set with C = {6, 12, 18}; intersection keeps only elements common to both sets. The common elements are 6 and 12, while 18 is absent from A ∪ B. Therefore, (A ∪ B) ∩ C = {6, 12}.
Frequently asked questions
What is the correct answer to this question?
{6, 12}
Why is this the correct answer?
First form the union A ∪ B by listing every element that occurs in either A or B, without repeating any element. This gives {2, 3, 4, 6, 8, 9, 10, 12, 15}. Now intersect this set with C = {6, 12, 18}; intersection keeps only elements common to both sets. The common elements are 6 and 12, while 18 is absent from A ∪ B. Therefore, (A ∪ B) ∩ C = {6, 12}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
