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

If sets A, B, and C satisfy A ⊆ B and B ∩ C = ∅, what is A ∩ C?

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Answer and explanation

Correct answer: ∅

Because A ⊆ B, every element of A is also an element of B. The condition B ∩ C = ∅ says that B and C have no common elements. Consequently, no element of A can belong to C either, because any such element would also belong to B and would contradict the disjointness of B and C. Hence A ∩ C = ∅.

Tags

setssubsetdisjoint-setsintersectionoperations-on-setsOperations on Sets (UnionDifference)operations on sets union intersection differenceMathematics

Frequently asked questions

What is the correct answer to this question?

∅

Why is this the correct answer?

Because A ⊆ B, every element of A is also an element of B. The condition B ∩ C = ∅ says that B and C have no common elements. Consequently, no element of A can belong to C either, because any such element would also belong to B and would contradict the disjointness of B and C. Hence A ∩ C = ∅.

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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