The universal set U contains 50 students. If n(A) = 18, n(B) = 22, and n(A ∩ B) = 7, how many students are outside A ∪ B?
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Answer and explanation
Correct answer: 17
To count students in A ∪ B, use the inclusion–exclusion formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Thus, n(A ∪ B) = 18 + 22 − 7 = 33. The universal set has 50 students, so those outside the union number 50 − 33 = 17. The intersection is subtracted because students belonging to both sets were counted twice.
Frequently asked questions
What is the correct answer to this question?
17
Why is this the correct answer?
To count students in A ∪ B, use the inclusion–exclusion formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Thus, n(A ∪ B) = 18 + 22 − 7 = 33. The universal set has 50 students, so those outside the union number 50 − 33 = 17. The intersection is subtracted because students belonging to both sets were counted twice.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
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