If n(A − B) = 17, n(B − C) = 22, and B − C has 6 elements common with A, what is n((A − B) ∪ (B − C))?
Answer and explanation
Correct answer: 39
Although B − C has 6 elements that also belong to A, none of these elements can belong to A − B, because every element of A − B is specifically outside B, whereas every element of B − C is inside B. Thus (A − B) and (B − C) are disjoint. Therefore, n((A − B) ∪ (B − C)) = 17 + 22 = 39. The stated common elements with A do not create an intersection between the two sets in the union.
Frequently asked questions
What is the correct answer to this question?
39
Why is this the correct answer?
Although B − C has 6 elements that also belong to A, none of these elements can belong to A − B, because every element of A − B is specifically outside B, whereas every element of B − C is inside B. Thus (A − B) and (B − C) are disjoint. Therefore, n((A − B) ∪ (B − C)) = 17 + 22 = 39. The stated common elements with A do not create an intersection between the two sets in the union.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
