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Class 10MathematicsSetsVenn DiagramsMediumLevel 14

Among 72 students, 34 like Mathematics, 31 like Physics, and 13 like both subjects. How many like neither subject?

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Answer and explanation

Correct answer: 20

Let M be the set of students who like Mathematics and P the set who like Physics. By the inclusion–exclusion principle, n(M union P) = n(M) + n(P) − n(M intersection P) = 34 + 31 − 13 = 52. Therefore, the number who like neither subject is the total number minus the union: 72 − 52 = 20. Hence option B is correct.

Tags

setsvenn diagramsneither setcardinalityMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

20

Why is this the correct answer?

Let M be the set of students who like Mathematics and P the set who like Physics. By the inclusion–exclusion principle, n(M union P) = n(M) + n(P) − n(M intersection P) = 34 + 31 − 13 = 52. Therefore, the number who like neither subject is the total number minus the union: 72 − 52 = 20. Hence option B 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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