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

In a group, 20 students like Mathematics, 15 like Science, and 8 like both. How many like only Mathematics?

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Answer and explanation

Correct answer: 12

Let M represent students who like Mathematics and S represent students who like Science. The 20 students in M include the 8 students who like both subjects. To count only Mathematics, remove the overlap: n(M − S) = n(M) − n(M ∩ S) = 20 − 8 = 12. Thus, 12 students like Mathematics but do not like Science.

Tags

setsdifferencecardinalityword-problemoverlapOperations on Sets (UnionIntersectionDifference)operations on sets union intersection differenceMathematics

Frequently asked questions

What is the correct answer to this question?

12

Why is this the correct answer?

Let M represent students who like Mathematics and S represent students who like Science. The 20 students in M include the 8 students who like both subjects. To count only Mathematics, remove the overlap: n(M − S) = n(M) − n(M ∩ S) = 20 − 8 = 12. Thus, 12 students like Mathematics but do not like Science.

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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