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

If A ∩ B ⊆ C, which of the following sets must be empty?

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Answer and explanation

Correct answer: (A ∩ B) \ C

The statement A ∩ B ⊆ C means that every element belonging to both A and B also belongs to C. Therefore, there cannot be any element of A ∩ B that lies outside C. The difference set (A ∩ B) \ C contains exactly those elements of A ∩ B that are not in C, so it must be the empty set, ∅.

Tags

setssubsetsset-differenceintersectionempty-setOperations on Sets (UnionDifference)operations on sets union intersection differenceMathematics

Frequently asked questions

What is the correct answer to this question?

(A ∩ B) \ C

Why is this the correct answer?

The statement A ∩ B ⊆ C means that every element belonging to both A and B also belongs to C. Therefore, there cannot be any element of A ∩ B that lies outside C. The difference set (A ∩ B) \ C contains exactly those elements of A ∩ B that are not in C, so it must be the empty set, ∅.

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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