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Subjects
Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)EasyLevel 10

In a class of 42 students, 24 like mathematics, 18 like science, and 7 like both subjects. How many students like at least one subject?

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Answer and explanation

Correct answer: 35

Let M be the set of students who like mathematics and S the set who like science. Students who like at least one subject belong to M ∪ S. By inclusion–exclusion, n(M ∪ S) = n(M) + n(S) − n(M ∩ S) = 24 + 18 − 7 = 35. The 7 students are subtracted once because they were counted twice.

Tags

setsunioninclusion-exclusionvenn-diagramsOperations on Sets (UnionIntersectionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

35

Why is this the correct answer?

Let M be the set of students who like mathematics and S the set who like science. Students who like at least one subject belong to M ∪ S. By inclusion–exclusion, n(M ∪ S) = n(M) + n(S) − n(M ∩ S) = 24 + 18 − 7 = 35. The 7 students are subtracted once because they were counted twice.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).

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