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Subjects
Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)EasyLevel 18

If A = {p, q, r} and B = {q, r, s}, what is A ∪ (A ∩ B)?

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Answer and explanation

Correct answer: {p, q, r}

The common elements of A and B are q and r, so A ∩ B = {q, r}. These elements are already contained in A = {p, q, r}. Taking the union of A with a subset of A adds nothing new. Therefore, A ∪ (A ∩ B) = A = {p, q, r}. This is the absorption identity A ∪ (A ∩ B) = A.

Tags

setsunionintersectionabsorption-lawOperations on Sets (UnionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

{p, q, r}

Why is this the correct answer?

The common elements of A and B are q and r, so A ∩ B = {q, r}. These elements are already contained in A = {p, q, r}. Taking the union of A with a subset of A adds nothing new. Therefore, A ∪ (A ∩ B) = A = {p, q, r}. This is the absorption identity A ∪ (A ∩ B) = A.

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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