If n(U) = 95, n(A') = 47, n(B') = 52, and n(A ∩ B) = 18, choose the correct value of n(A ∪ B).
Advertisement
Answer and explanation
Correct answer: 73
The universal set has 95 elements. Therefore, n(A) = 95 − 47 = 48 and n(B) = 95 − 52 = 43. Applying the two-set union formula gives n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 48 + 43 − 18 = 73. The intersection is subtracted once because it was counted in both set totals. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
73
Why is this the correct answer?
The universal set has 95 elements. Therefore, n(A) = 95 − 47 = 48 and n(B) = 95 − 52 = 43. Applying the two-set union formula gives n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 48 + 43 − 18 = 73. The intersection is subtracted once because it was counted in both set totals. Hence 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).
Advertisement