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Class 10MathematicsSetsComplement of a Set and Its PropertiesEasyLevel 14

If U = {a, b, c, d, e, f}, A = {a, b, d}, and B = {b, c, d}, what is (A ∪ B)'?

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Answer and explanation

Correct answer: {e, f}

First form the union by listing every element that occurs in A or B: A ∪ B = {a, b, c, d}. The complement of this union contains the elements of U that are absent from it. In U, those remaining elements are e and f. Hence (A ∪ B)' = {e, f}. This also agrees with De Morgan’s law: (A ∪ B)' = A' ∩ B'.

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setsunioncomplementDe Morgan lawVenn diagramsComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

{e, f}

Why is this the correct answer?

First form the union by listing every element that occurs in A or B: A ∪ B = {a, b, c, d}. The complement of this union contains the elements of U that are absent from it. In U, those remaining elements are e and f. Hence (A ∪ B)' = {e, f}. This also agrees with De Morgan’s law: (A ∪ B)' = A' ∩ B'.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.

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