If n(A∩B)=24 and n(A∩B∩C)=9, how many elements are only in A and B but not in C?
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Answer and explanation
Correct answer: 15
The value n(A∩B)=24 includes two kinds of elements: those in A and B but not C, and those in all three sets. The latter group has 9 elements. Therefore, the number only in A and B is n(A∩B)−n(A∩B∩C)=24−9=15. Thus option C is correct; simply using 24 would incorrectly include the triple intersection.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
The value n(A∩B)=24 includes two kinds of elements: those in A and B but not C, and those in all three sets. The latter group has 9 elements. Therefore, the number only in A and B is n(A∩B)−n(A∩B∩C)=24−9=15. Thus option C is correct; simply using 24 would incorrectly include the triple intersection.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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