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Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)MediumLevel 10

If n(A ∪ B) = 20, n(A) = 12, and n(B) = 11, what is n(A ∩ B)?

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Answer and explanation

Correct answer: 3

For two finite sets, n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Rearrange the formula to find the intersection: n(A ∩ B) = n(A) + n(B) − n(A ∪ B). Substitution gives 12 + 11 − 20 = 3. Thus the two sets have three common elements, and option C is the unique correct answer.

Tags

setscardinalityintersectioninclusion-exclusionOperations on Sets (UnionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

3

Why is this the correct answer?

For two finite sets, n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Rearrange the formula to find the intersection: n(A ∩ B) = n(A) + n(B) − n(A ∪ B). Substitution gives 12 + 11 − 20 = 3. Thus the two sets have three common elements, and option C is the unique correct answer.

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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