In a class, 58 students learn music, 49 learn painting, and 22 learn both. How many students learn at least one of the two arts?
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Answer and explanation
Correct answer: 85
At least one of the two arts means the union of the music and painting groups. By the two-set inclusion–exclusion formula, n(M∪P)=n(M)+n(P)−n(M∩P). Therefore, n(M∪P)=58+49−22=85. The 22 students who learn both are subtracted once because they were counted in both 58 and 49.
Frequently asked questions
What is the correct answer to this question?
85
Why is this the correct answer?
At least one of the two arts means the union of the music and painting groups. By the two-set inclusion–exclusion formula, n(M∪P)=n(M)+n(P)−n(M∩P). Therefore, n(M∪P)=58+49−22=85. The 22 students who learn both are subtracted once because they were counted in both 58 and 49.
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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