If A = {1, 2, 3, 4, 5} and B = {2, 4, 6}, what is (A ∪ B) − (A ∩ B)?
Answer and explanation
Correct answer: {1, 3, 5, 6}
First calculate the union and intersection. A ∪ B = {1, 2, 3, 4, 5, 6}, while A ∩ B = {2, 4}. Subtracting the intersection from the union removes the common elements 2 and 4, leaving {1, 3, 5, 6}. This operation gives the elements belonging to exactly one of the two sets, also called their symmetric difference. Hence, option B is correct.
Frequently asked questions
What is the correct answer to this question?
{1, 3, 5, 6}
Why is this the correct answer?
First calculate the union and intersection. A ∪ B = {1, 2, 3, 4, 5, 6}, while A ∩ B = {2, 4}. Subtracting the intersection from the union removes the common elements 2 and 4, leaving {1, 3, 5, 6}. This operation gives the elements belonging to exactly one of the two sets, also called their symmetric difference. Hence, option B 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).
