If n(A) = 30, n(B) = 28, and n(A ∪ B) = 52, what is n(A − B)?
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Answer and explanation
Correct answer: 24
Use the inclusion–exclusion formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Hence, 52 = 30 + 28 − n(A ∩ B), so n(A ∩ B) = 6. The set A − B contains elements that are in A but not in B. Therefore, n(A − B) = n(A) − n(A ∩ B) = 30 − 6 = 24. Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
24
Why is this the correct answer?
Use the inclusion–exclusion formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Hence, 52 = 30 + 28 − n(A ∩ B), so n(A ∩ B) = 6. The set A − B contains elements that are in A but not in B. Therefore, n(A − B) = n(A) − n(A ∩ B) = 30 − 6 = 24. Thus 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).
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