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Class 12MathematicsSetsMediumLevel 11
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If n(A ∩ Bᶜ) = 44, n(Aᶜ ∩ B) = 36, and n(A △ B) = 92, what is the correct conclusion about the data?

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Answer and explanation

Correct answer: The data are inconsistent

The symmetric difference \(A\triangle B\) contains elements belonging to exactly one of the two sets. Therefore \(A\triangle B=(A\cap B^c)\cup(A^c\cap B)\), and the two parts are disjoint. Its cardinality must be \(44+36=80\), not 92. Thus the stated values cannot all be true together, so option A is correct.

Related tags

SetsSymmetric DifferenceVenn DiagramsData ConsistencyMathematicsClass 12 Mcq

Frequently asked questions

What is the correct answer to this question?

The data are inconsistent

Why is this the correct answer?

The symmetric difference \(A\triangle B\) contains elements belonging to exactly one of the two sets. Therefore \(A\triangle B=(A\cap B^c)\cup(A^c\cap B)\), and the two parts are disjoint. Its cardinality must be \(44+36=80\), not 92. Thus the stated values cannot all be true together, so option A is correct.

Which subject and chapter does this question cover?

This is a Class 12 Mathematics question. Chapter: Sets.

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