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

If A ⊆ C and B ⊆ C, what is (A ∪ B) \ C?

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Answer and explanation

Correct answer: ∅

Since A ⊆ C and B ⊆ C, every element of A and every element of B is already in C. Therefore, every element of A ∪ B is also in C, which means A ∪ B ⊆ C. The difference (A ∪ B) \ C asks for elements in A ∪ B that are outside C. There are none, so the result is the empty set ∅.

Tags

setssubsetuniondifferenceempty-setOperations on Sets (UnionIntersectionDifference)operations on sets union intersection differenceMathematics

Frequently asked questions

What is the correct answer to this question?

∅

Why is this the correct answer?

Since A ⊆ C and B ⊆ C, every element of A and every element of B is already in C. Therefore, every element of A ∪ B is also in C, which means A ∪ B ⊆ C. The difference (A ∪ B) \ C asks for elements in A ∪ B that are outside C. There are none, so the result is 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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