If A = {2, 3, 5, 7}, B = {1, 3, 5, 9}, and C = {3, 4, 5}, what is (A ∩ B) ∪ C?
Answer and explanation
Correct answer: {3, 4, 5}
First calculate A ∩ B, the set of elements common to A and B. The common elements are 3 and 5, so A ∩ B = {3, 5}. Now take the union of this result with C = {3, 4, 5}. Including every distinct element gives {3, 5} ∪ {3, 4, 5} = {3, 4, 5}. Therefore, option B is correct. Elements such as 2, 7, 1, and 9 are not included because they are not in the intermediate intersection or in C.
Frequently asked questions
What is the correct answer to this question?
{3, 4, 5}
Why is this the correct answer?
First calculate A ∩ B, the set of elements common to A and B. The common elements are 3 and 5, so A ∩ B = {3, 5}. Now take the union of this result with C = {3, 4, 5}. Including every distinct element gives {3, 5} ∪ {3, 4, 5} = {3, 4, 5}. Therefore, option B is correct. Elements such as 2, 7, 1, and 9 are not included because they are not in the intermediate intersection or in C.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
