If n(A ∪ B) = 12, n(A) = 7, and n(B) = 8, what is n(A ∩ B)?
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Answer and explanation
Correct answer: 3
Use the union formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given values gives 12 = 7 + 8 − n(A ∩ B), or 12 = 15 − n(A ∩ B). Rearranging, n(A ∩ B) = 15 − 12 = 3. Therefore, option C is correct and the two sets have three common elements.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
Use the union formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given values gives 12 = 7 + 8 − n(A ∩ B), or 12 = 15 − n(A ∩ B). Rearranging, n(A ∩ B) = 15 − 12 = 3. Therefore, option C is correct and the two sets have three common elements.
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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