In a survey, n(U)=120, n(A)=61, n(B)=54, and n(A∩B)=25. How many elements are in neither set?
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Answer and explanation
Correct answer: 30
First calculate the union using n(A∪B)=n(A)+n(B)−n(A∩B). Thus, n(A∪B)=61+54−25=90. The elements in neither A nor B are outside the union, so their number is n(U)−n(A∪B)=120−90=30. Equivalently, they form the complement of A∪B within U. Therefore, option C is correct.
Frequently asked questions
What is the correct answer to this question?
30
Why is this the correct answer?
First calculate the union using n(A∪B)=n(A)+n(B)−n(A∩B). Thus, n(A∪B)=61+54−25=90. The elements in neither A nor B are outside the union, so their number is n(U)−n(A∪B)=120−90=30. Equivalently, they form the complement of A∪B within U. Therefore, option C 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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