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Subjects
Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)EasyLevel 18

In a class, 22 students like drawing, 16 like music, and 6 like both. How many students like at least one activity?

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Answer and explanation

Correct answer: 32

Let D be the set of students who like drawing and M the set who like music. Students liking at least one activity are in D ∪ M. By the inclusion-exclusion formula, n(D ∪ M) = n(D) + n(M) − n(D ∩ M) = 22 + 16 − 6 = 32. We subtract the 6 students who like both because they were counted twice.

Tags

setsunioncardinalityinclusion-exclusionOperations on Sets (UnionIntersectionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

32

Why is this the correct answer?

Let D be the set of students who like drawing and M the set who like music. Students liking at least one activity are in D ∪ M. By the inclusion-exclusion formula, n(D ∪ M) = n(D) + n(M) − n(D ∩ M) = 22 + 16 − 6 = 32. We subtract the 6 students who like both 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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