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Subjects
Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)HardLevel 10

If A ∪ B = B ∪ C and A ∩ B = B ∩ C, which conclusion must be true?

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Answer and explanation

Correct answer: A = C

Consider any element x. If x is not in B, the union equality gives x ∈ A exactly when x ∈ C. If x is in B, the intersection equality gives x ∈ A exactly when x ∈ C. Thus every element belongs to A precisely when it belongs to C, so A = C. The other options do not necessarily follow.

Tags

setsunionintersectionset-equalityoperations-on-setsOperations on Sets (UnionDifference)operations on sets union intersection differenceMathematics

Frequently asked questions

What is the correct answer to this question?

A = C

Why is this the correct answer?

Consider any element x. If x is not in B, the union equality gives x ∈ A exactly when x ∈ C. If x is in B, the intersection equality gives x ∈ A exactly when x ∈ C. Thus every element belongs to A precisely when it belongs to C, so A = C. The other options do not necessarily follow.

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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