If n(A) = 49, n(B) = 52, and A ∩ B = ∅, how many elements belong to exactly one of the two sets?
Answer and explanation
Correct answer: 101
Since A ∩ B = ∅, the two sets are disjoint and have no common elements. Therefore, every element of A and every element of B belongs to exactly one of the two sets. The required number is n(A) + n(B) = 49 + 52 = 101. Thus, option D is correct; subtracting the two cardinalities or choosing only one set would not represent the total number of elements in exactly one set.
Frequently asked questions
What is the correct answer to this question?
101
Why is this the correct answer?
Since A ∩ B = ∅, the two sets are disjoint and have no common elements. Therefore, every element of A and every element of B belongs to exactly one of the two sets. The required number is n(A) + n(B) = 49 + 52 = 101. Thus, option D is correct; subtracting the two cardinalities or choosing only one set would not represent the total number of elements in exactly one set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
