In a Venn diagram, n(A−B)=31, n(B−A)=37, n(A∩B)=24, and n((A∪B)ᶜ)=18. What is n(Aᶜ)?
Answer and explanation
Correct answer: 55
The complement Aᶜ contains every element that is not in A. In the two-set Venn diagram, these are precisely the elements in B−A together with the elements outside A∪B. The given counts are 37 and 18, respectively. Therefore, n(Aᶜ)=n(B−A)+n((A∪B)ᶜ)=37+18=55. The other regions either belong to A or are not outside A.
Frequently asked questions
What is the correct answer to this question?
55
Why is this the correct answer?
The complement Aᶜ contains every element that is not in A. In the two-set Venn diagram, these are precisely the elements in B−A together with the elements outside A∪B. The given counts are 37 and 18, respectively. Therefore, n(Aᶜ)=n(B−A)+n((A∪B)ᶜ)=37+18=55. The other regions either belong to A or are not outside A.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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