If n(A)=80, n(A∩B)=35, n(A∩C)=32, and n(A∩B∩C)=14, how many elements are only in A?
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Answer and explanation
Correct answer: 27
To obtain the region only in A, subtract from n(A) the elements shared with B and the elements shared with C. The triple intersection has been subtracted twice, so add it once: only A=80−35−32+14=27. Thus 27 elements are in A but not in B or C. Simply calculating 80−35−32=13 would incorrectly remove the triple-overlap twice.
Frequently asked questions
What is the correct answer to this question?
27
Why is this the correct answer?
To obtain the region only in A, subtract from n(A) the elements shared with B and the elements shared with C. The triple intersection has been subtracted twice, so add it once: only A=80−35−32+14=27. Thus 27 elements are in A but not in B or C. Simply calculating 80−35−32=13 would incorrectly remove the triple-overlap twice.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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