If n(U)=96, n(A−B)=29, n(A∩B)=17, and n(B−A)=22, what is the number of elements outside A∪B in the Venn diagram?
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Answer and explanation
Correct answer: 28
The union A∪B consists of three disjoint regions: elements only in A, common elements, and elements only in B. Therefore, n(A∪B)=n(A−B)+n(A∩B)+n(B−A)=29+17+22=68. The universal set has 96 elements, so the outside region contains 96−68=28 elements. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
28
Why is this the correct answer?
The union A∪B consists of three disjoint regions: elements only in A, common elements, and elements only in B. Therefore, n(A∪B)=n(A−B)+n(A∩B)+n(B−A)=29+17+22=68. The universal set has 96 elements, so the outside region contains 96−68=28 elements. Hence option A 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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