If n(A ∩ B) = 0, n(A) = 39, and n(B) = 48, what is n(A △ B)?
Answer and explanation
Correct answer: 87
The symmetric difference A △ B consists of elements that belong to A or B but not to both. Since n(A ∩ B) = 0, the sets are disjoint, so every element of A and every element of B belongs to the symmetric difference. Therefore n(A △ B) = n(A) + n(B) = 39 + 48 = 87. Option A is correct. In general, n(A △ B) = n(A) + n(B) − 2n(A ∩ B).
Frequently asked questions
What is the correct answer to this question?
87
Why is this the correct answer?
The symmetric difference A △ B consists of elements that belong to A or B but not to both. Since n(A ∩ B) = 0, the sets are disjoint, so every element of A and every element of B belongs to the symmetric difference. Therefore n(A △ B) = n(A) + n(B) = 39 + 48 = 87. Option A is correct. In general, n(A △ B) = n(A) + n(B) − 2n(A ∩ B).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
