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

If A and B are subsets of a universal set U, then (A \ B) ∪ (A ∩ B) is equal to which set?

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Answer and explanation

Correct answer: A

Consider any element x of A. If x is not in B, then x belongs to A \ B. If x is in B, then x belongs to A ∩ B. These two cases cover every element of A, and both resulting sets contain only elements of A. Therefore their union is exactly A. This is the partition identity A = (A \ B) ∪ (A ∩ B).

Tags

setsset-differenceintersectionset-identitiesOperations on Sets (UnionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

A

Why is this the correct answer?

Consider any element x of A. If x is not in B, then x belongs to A \ B. If x is in B, then x belongs to A ∩ B. These two cases cover every element of A, and both resulting sets contain only elements of A. Therefore their union is exactly A. This is the partition identity A = (A \ B) ∪ (A ∩ 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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