If A = {1, 2, 3, 4}, B = {3, 4, 5}, and C = {4, 5, 6}, what is (A ∩ B) ∪ C?
Answer and explanation
Correct answer: {3, 4, 5, 6}
The parentheses require us to find A ∩ B first. The elements common to A = {1, 2, 3, 4} and B = {3, 4, 5} are {3, 4}. Now take the union with C = {4, 5, 6}: {3, 4} ∪ {4, 5, 6} = {3, 4, 5, 6}. Element 4 is written once, and 1 and 2 are not included because they are not in the intermediate intersection.
Frequently asked questions
What is the correct answer to this question?
{3, 4, 5, 6}
Why is this the correct answer?
The parentheses require us to find A ∩ B first. The elements common to A = {1, 2, 3, 4} and B = {3, 4, 5} are {3, 4}. Now take the union with C = {4, 5, 6}: {3, 4} ∪ {4, 5, 6} = {3, 4, 5, 6}. Element 4 is written once, and 1 and 2 are not included because they are not in the intermediate intersection.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
