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Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)MediumLevel 16

If A and B are any two sets, then (A ∪ B) \ (A \ B) is equal to which set?

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Answer and explanation

Correct answer: B

Separate the elements of A ∪ B into three disjoint regions: A \ B, A ∩ B, and B \ A. Subtracting A \ B removes only the elements that belong exclusively to A. The remaining two regions, A ∩ B and B \ A, together contain every element of B and no element outside B. Therefore, (A ∪ B) \ (A \ B) = B.

Tags

setsuniondifferenceset-identityOperations on Sets (UnionIntersectionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

B

Why is this the correct answer?

Separate the elements of A ∪ B into three disjoint regions: A \ B, A ∩ B, and B \ A. Subtracting A \ B removes only the elements that belong exclusively to A. The remaining two regions, A ∩ B and B \ A, together contain every element of B and no element outside B. Therefore, (A ∪ B) \ (A \ B) = B.

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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