If A ∩ B = ∅, n(A) = 21, and n(B) = 17, what is the value of n(A ∪ B)?
Answer and explanation
Correct answer: 38
The condition A ∩ B = ∅ means that A and B are disjoint, so they have no common elements. For any two finite sets, n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given values gives n(A ∪ B) = 21 + 17 − 0 = 38. Equivalently, because no element is counted twice, we can simply add the two cardinalities. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
38
Why is this the correct answer?
The condition A ∩ B = ∅ means that A and B are disjoint, so they have no common elements. For any two finite sets, n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given values gives n(A ∪ B) = 21 + 17 − 0 = 38. Equivalently, because no element is counted twice, we can simply add the two cardinalities. Therefore, 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).
