If A∩B=∅, n(A)=45, and n(B)=37, what is n(A∪B)?
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Answer and explanation
Correct answer: 82
The condition A∩B=∅ means that A and B are disjoint; they have no common elements. The general formula is n(A∪B)=n(A)+n(B)−n(A∩B). Since the intersection has zero elements, n(A∪B)=45+37−0=82. Therefore option D is correct. Adding the two cardinalities is valid here precisely because the sets do not overlap.
Frequently asked questions
What is the correct answer to this question?
82
Why is this the correct answer?
The condition A∩B=∅ means that A and B are disjoint; they have no common elements. The general formula is n(A∪B)=n(A)+n(B)−n(A∩B). Since the intersection has zero elements, n(A∪B)=45+37−0=82. Therefore option D is correct. Adding the two cardinalities is valid here precisely because the sets do not overlap.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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