If, in three sets, 84 elements are in exactly one set, 63 elements are in exactly two sets, and 18 elements are in all three sets, what is n(A∪B∪C)?
Answer and explanation
Correct answer: 165
The phrases “exactly one,” “exactly two,” and “all three” refer to mutually exclusive regions of the Venn diagram. Their union is the complete set of elements belonging to at least one of A, B, or C. Therefore, n(A∪B∪C)=84+63+18=165. No further inclusion–exclusion correction is needed because the three given counts are already disjoint categories.
Frequently asked questions
What is the correct answer to this question?
165
Why is this the correct answer?
The phrases “exactly one,” “exactly two,” and “all three” refer to mutually exclusive regions of the Venn diagram. Their union is the complete set of elements belonging to at least one of A, B, or C. Therefore, n(A∪B∪C)=84+63+18=165. No further inclusion–exclusion correction is needed because the three given counts are already disjoint categories.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
