If n(A)=63, n(A∩B)=26, n(A∩C)=24, and n(A∩B∩C)=9, how many elements are only in A?
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Answer and explanation
Correct answer: 22
To count elements only in A, subtract the elements shared with B and the elements shared with C, then add the triple intersection once because it was subtracted twice: only A = n(A)−n(A∩B)−n(A∩C)+n(A∩B∩C). Thus, only A = 63−26−24+9=22. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
22
Why is this the correct answer?
To count elements only in A, subtract the elements shared with B and the elements shared with C, then add the triple intersection once because it was subtracted twice: only A = n(A)−n(A∩B)−n(A∩C)+n(A∩B∩C). Thus, only A = 63−26−24+9=22. Therefore, option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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