If A = {1, 2, 3, 6}, B = {2, 3, 5, 6}, and C = {3, 6, 9}, what is A ∩ B ∩ C?
Answer and explanation
Correct answer: {3, 6}
The intersection A ∩ B ∩ C contains only those elements that occur in all three sets simultaneously. The element 3 occurs in A, B, and C, and the element 6 also occurs in A, B, and C. The elements 1, 2, 5, and 9 fail to occur in at least one of the sets. Therefore, A ∩ B ∩ C = {3, 6}, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
{3, 6}
Why is this the correct answer?
The intersection A ∩ B ∩ C contains only those elements that occur in all three sets simultaneously. The element 3 occurs in A, B, and C, and the element 6 also occurs in A, B, and C. The elements 1, 2, 5, and 9 fail to occur in at least one of the sets. Therefore, A ∩ B ∩ C = {3, 6}, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
