If only n(A − B) = 42, n(B − C) = 35, and n(C − A) = 31 are given, which conclusion cannot always be assumed true?
Answer and explanation
Correct answer: These values determine n(A ∪ B ∪ C).
The meaning of set difference is fixed: A − B contains elements in A but not B, and similarly for the other differences, so B, C, and D are always true. However, the three given counts do not reveal the pairwise overlaps, the triple overlap, or several exclusive regions. These unknown parts can change the union, so n(A ∪ B ∪ C) cannot always be determined. Therefore A is correct.
Frequently asked questions
What is the correct answer to this question?
These values determine n(A ∪ B ∪ C).
Why is this the correct answer?
The meaning of set difference is fixed: A − B contains elements in A but not B, and similarly for the other differences, so B, C, and D are always true. However, the three given counts do not reveal the pairwise overlaps, the triple overlap, or several exclusive regions. These unknown parts can change the union, so n(A ∪ B ∪ C) cannot always be determined. Therefore A 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).
