If A ∪ B = {2,4,6,8,10,12,14}, A − B = {2,10}, and B − A = {6,14}, what is A ∩ B?
Answer and explanation
Correct answer: {4,8,12}
Every element of A ∪ B belongs to exactly one of three disjoint regions: A − B, A ∩ B, or B − A. The union is {2,4,6,8,10,12,14}. Removing the elements belonging only to A, namely {2,10}, and those belonging only to B, namely {6,14}, leaves {4,8,12}. These remaining elements must belong to both sets, so A ∩ B = {4,8,12}.
Frequently asked questions
What is the correct answer to this question?
{4,8,12}
Why is this the correct answer?
Every element of A ∪ B belongs to exactly one of three disjoint regions: A − B, A ∩ B, or B − A. The union is {2,4,6,8,10,12,14}. Removing the elements belonging only to A, namely {2,10}, and those belonging only to B, namely {6,14}, leaves {4,8,12}. These remaining elements must belong to both sets, so A ∩ B = {4,8,12}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
