If n(A) = 36, n(B) = 42, and A intersection B is the empty set, how many elements are in exactly one set?
Answer and explanation
Correct answer: 78
Because A and B are disjoint, no element is counted in both sets. Consequently, every element of A belongs to exactly one set, and every element of B also belongs to exactly one set. The number of elements in exactly one of the two sets is therefore n(A) + n(B) = 36 + 42 = 78. Equivalently, the symmetric difference has size 78 because the intersection has size zero. Hence option D is correct.
Frequently asked questions
What is the correct answer to this question?
78
Why is this the correct answer?
Because A and B are disjoint, no element is counted in both sets. Consequently, every element of A belongs to exactly one set, and every element of B also belongs to exactly one set. The number of elements in exactly one of the two sets is therefore n(A) + n(B) = 36 + 42 = 78. Equivalently, the symmetric difference has size 78 because the intersection has size zero. Hence option D is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
