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Subjects
Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)MediumLevel 17

If A − B = ∅ and B − C = ∅, which conclusion is correct?

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Answer and explanation

Correct answer: A ⊆ C

A − B = ∅ means that no element of A lies outside B, so A ⊆ B. Likewise, B − C = ∅ means B ⊆ C. Subset inclusion is transitive: if every element of A is in B and every element of B is in C, then every element of A is in C. Therefore A ⊆ C must be true. Equality or disjointness is not forced.

Tags

setsset-differencesubsetstransitivityoperations-on-setsOperations on Sets (UnionIntersectionDifference)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?

A − B = ∅ means that no element of A lies outside B, so A ⊆ B. Likewise, B − C = ∅ means B ⊆ C. Subset inclusion is transitive: if every element of A is in B and every element of B is in C, then every element of A is in C. Therefore A ⊆ C must be true. Equality or disjointness is not forced.

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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