Given n(A − B) = 34, n(B − C) = 41, and n(C − A) = 29, which conclusion cannot always be assumed to be true?
Answer and explanation
Correct answer: These three values determine n(A ∪ B ∪ C).
The quantities n(A − B), n(B − C), and n(C − A) describe only three difference regions. They do not reveal the sizes of all pairwise intersections, the triple intersection, or portions such as A ∩ B but not C. Consequently, the total size of A ∪ B ∪ C cannot always be determined from these three numbers alone. Options B, C, and D are valid definitions.
Frequently asked questions
What is the correct answer to this question?
These three values determine n(A ∪ B ∪ C).
Why is this the correct answer?
The quantities n(A − B), n(B − C), and n(C − A) describe only three difference regions. They do not reveal the sizes of all pairwise intersections, the triple intersection, or portions such as A ∩ B but not C. Consequently, the total size of A ∪ B ∪ C cannot always be determined from these three numbers alone. Options B, C, and D are valid definitions.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
