In a class, 63 students learn dance, 58 learn music, and 26 learn both. How many students learn at least one art?
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Answer and explanation
Correct answer: 95
“At least one art” means the union of the dance and music groups. For two sets, n(D∪M)=n(D)+n(M)−n(D∩M), because students learning both are counted twice in the simple sum. Therefore n(D∪M)=63+58−26=95. Thus, 95 students learn at least one of the two arts, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
95
Why is this the correct answer?
“At least one art” means the union of the dance and music groups. For two sets, n(D∪M)=n(D)+n(M)−n(D∩M), because students learning both are counted twice in the simple sum. Therefore n(D∪M)=63+58−26=95. Thus, 95 students learn at least one of the two arts, so option A is correct.
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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