If n(A △ B) = 112 and n(A ∩ B) = 39, what is n(A ∪ B)?
Answer and explanation
Correct answer: 151
The symmetric difference A △ B contains the elements belonging to exactly one of the two sets, while A ∩ B contains the common elements. These regions are disjoint and together make the entire union: A ∪ B = (A △ B) ∪ (A ∩ B). Therefore n(A ∪ B) = 112 + 39 = 151. The common region must be added because it is excluded from the symmetric difference. Hence option C is correct.
Frequently asked questions
What is the correct answer to this question?
151
Why is this the correct answer?
The symmetric difference A △ B contains the elements belonging to exactly one of the two sets, while A ∩ B contains the common elements. These regions are disjoint and together make the entire union: A ∪ B = (A △ B) ∪ (A ∩ B). Therefore n(A ∪ B) = 112 + 39 = 151. The common region must be added because it is excluded from the symmetric difference. Hence option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
