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Subjects
Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)EasyLevel 17

In a class, 18 students play cricket, 12 play football, and 5 play both. How many students play at least one game?

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Answer and explanation

Correct answer: 25

Let C be the set of cricket players and F the set of football players. Students who play at least one game belong to C ∪ F. By the inclusion–exclusion formula, n(C ∪ F) = n(C) + n(F) − n(C ∩ F) = 18 + 12 − 5 = 25. The five students who play both were counted twice, so they must be subtracted once.

Tags

setsunioncardinalityinclusion-exclusionword-problemOperations on Sets (UnionIntersectionDifference)operations on sets union intersection differenceMathematics

Frequently asked questions

What is the correct answer to this question?

25

Why is this the correct answer?

Let C be the set of cricket players and F the set of football players. Students who play at least one game belong to C ∪ F. By the inclusion–exclusion formula, n(C ∪ F) = n(C) + n(F) − n(C ∩ F) = 18 + 12 − 5 = 25. The five students who play both were counted twice, so they must be subtracted once.

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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