If A ∩ B = B ∩ C = C ∩ A = ∅, |A| = 9, |B| = 11, and |C| = 13, what is |A ∪ B ∪ C|?
Answer and explanation
Correct answer: 33
The three pairwise intersection conditions show that no element is shared by any two of the sets. Thus A, B, and C are pairwise disjoint. For disjoint finite sets, the cardinality of their union is the sum of their cardinalities, because no element is counted twice. Therefore |A ∪ B ∪ C| = 9 + 11 + 13 = 33, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
33
Why is this the correct answer?
The three pairwise intersection conditions show that no element is shared by any two of the sets. Thus A, B, and C are pairwise disjoint. For disjoint finite sets, the cardinality of their union is the sum of their cardinalities, because no element is counted twice. Therefore |A ∪ B ∪ C| = 9 + 11 + 13 = 33, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
