If n(A) = 55, n(B) = 62, and n(A − B) = 23, what is n(A ∪ B)?
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Answer and explanation
Correct answer: 85
The difference A − B represents the elements in A but not in B. Hence the number common to A and B is n(A ∩ B) = n(A) − n(A − B) = 55 − 23 = 32. Applying inclusion–exclusion, n(A ∪ B) = 55 + 62 − 32 = 85. The sum 117 would count the 32 common elements twice, so it is not the union size.
Frequently asked questions
What is the correct answer to this question?
85
Why is this the correct answer?
The difference A − B represents the elements in A but not in B. Hence the number common to A and B is n(A ∩ B) = n(A) − n(A − B) = 55 − 23 = 32. Applying inclusion–exclusion, n(A ∪ B) = 55 + 62 − 32 = 85. The sum 117 would count the 32 common elements twice, so it is not the union size.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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