If n(A)=60, n(B)=55, and n(A∩B)=25, how many elements belong to exactly one set?
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Answer and explanation
Correct answer: 65
Elements in exactly one set are those in A but not B together with those in B but not A. Thus only A has 60−25=35 elements and only B has 55−25=30 elements. Their total is 35+30=65. Equivalently, the formula is n(A)+n(B)−2n(A∩B)=60+55−50=65. The union, 90, would include the intersection as well.
Frequently asked questions
What is the correct answer to this question?
65
Why is this the correct answer?
Elements in exactly one set are those in A but not B together with those in B but not A. Thus only A has 60−25=35 elements and only B has 55−25=30 elements. Their total is 35+30=65. Equivalently, the formula is n(A)+n(B)−2n(A∩B)=60+55−50=65. The union, 90, would include the intersection as well.
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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