In a survey, n(U) = 120, n(A) = 72, n(B) = 65, and n(A ∩ B) = 38. How many students are only in A?
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Answer and explanation
Correct answer: 34
“Only in A” means the elements belonging to A but not to B, represented by A − B or A ∩ Bᶜ. The total number in A includes the 38 students who are also in B. Therefore, subtract the intersection from A: n(A − B) = n(A) − n(A ∩ B) = 72 − 38 = 34. Thus, option A is correct.
Frequently asked questions
What is the correct answer to this question?
34
Why is this the correct answer?
“Only in A” means the elements belonging to A but not to B, represented by A − B or A ∩ Bᶜ. The total number in A includes the 38 students who are also in B. Therefore, subtract the intersection from A: n(A − B) = n(A) − n(A ∩ B) = 72 − 38 = 34. Thus, 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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