If in three sets there are 71 elements belonging to exactly one set, 46 elements belonging to exactly two sets, and 15 elements belonging to all three sets, what is n(A ∪ B ∪ C)?
Answer and explanation
Correct answer: 132
The three categories are mutually exclusive and together cover every element in the union: elements in exactly one set, elements in exactly two sets, and elements in all three sets. Therefore no inclusion–exclusion correction is needed. Add the category counts directly: n(A ∪ B ∪ C) = 71 + 46 + 15 = 132. Option B would omit the elements belonging to all three sets, so option C is the unique correct answer.
Frequently asked questions
What is the correct answer to this question?
132
Why is this the correct answer?
The three categories are mutually exclusive and together cover every element in the union: elements in exactly one set, elements in exactly two sets, and elements in all three sets. Therefore no inclusion–exclusion correction is needed. Add the category counts directly: n(A ∪ B ∪ C) = 71 + 46 + 15 = 132. Option B would omit the elements belonging to all three sets, so option C is the unique correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
