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Class 10MathematicsSetsVenn DiagramsMediumLevel 13

In a survey, n(U) = 80, n(A) = 45, n(B) = 37, and n(A ∩ B) = 18. How many students are in neither group?

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Answer and explanation

Correct answer: 16

First calculate the number in at least one group: n(A ∪ B) = 45 + 37 − 18 = 64. Students in neither group are outside the union but still inside the universal set U. Hence, neither = n(U) − n(A ∪ B) = 80 − 64 = 16. Therefore, option A is correct; 64 is the number in at least one group, not the number outside both.

Tags

setscomplementunionvenn-diagramsVenn DiagramsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

16

Why is this the correct answer?

First calculate the number in at least one group: n(A ∪ B) = 45 + 37 − 18 = 64. Students in neither group are outside the union but still inside the universal set U. Hence, neither = n(U) − n(A ∪ B) = 80 − 64 = 16. Therefore, option A is correct; 64 is the number in at least one group, not the number outside both.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.

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