Among 100 students, 40 are only in A, 28 are only in B, and 12 are in both. How many are in at least one set?
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Answer and explanation
Correct answer: 80
The phrase “at least one” means belonging to A or B or both, which is the union A ∪ B. The problem already gives three separate, non-overlapping regions: only A has 40 students, only B has 28, and both sets have 12. Therefore, n(A ∪ B) = 40 + 28 + 12 = 80. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
80
Why is this the correct answer?
The phrase “at least one” means belonging to A or B or both, which is the union A ∪ B. The problem already gives three separate, non-overlapping regions: only A has 40 students, only B has 28, and both sets have 12. Therefore, n(A ∪ B) = 40 + 28 + 12 = 80. 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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