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Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 19

If A is a subset of U, what is (U minus A)' equal to, where complements are taken with respect to U?

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Answer and explanation

Correct answer: A

For a subset A of U, the relative difference U minus A is exactly the complement A'. Taking the complement once more gives (A')'. By the double-complement law, the complement of the complement of A is A itself. Therefore (U minus A)' = (A')' = A, making option A correct.

Tags

setsset-differencedouble-complementcomplement-lawsComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

A

Why is this the correct answer?

For a subset A of U, the relative difference U minus A is exactly the complement A'. Taking the complement once more gives (A')'. By the double-complement law, the complement of the complement of A is A itself. Therefore (U minus A)' = (A')' = A, making option A correct.

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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