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Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 10

Let U = {1,2,3,4,5,6,7,8,9,10}, A = {1,2,3,4,5}, and B = {4,5,6,7,8}. What is Aᶜ − Bᶜ?

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Answer and explanation

Correct answer: {6,7,8}

All complements are taken with respect to U. Thus Aᶜ = {6,7,8,9,10}, while Bᶜ = {1,2,3,9,10}. The difference Aᶜ − Bᶜ consists of elements present in Aᶜ but absent from Bᶜ. Removing 9 and 10 from Aᶜ leaves {6,7,8}. Equivalently, Aᶜ − Bᶜ = Aᶜ ∩ B. Therefore, option A is correct.

Tags

setscomplementset differenceset identityComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

{6,7,8}

Why is this the correct answer?

All complements are taken with respect to U. Thus Aᶜ = {6,7,8,9,10}, while Bᶜ = {1,2,3,9,10}. The difference Aᶜ − Bᶜ consists of elements present in Aᶜ but absent from Bᶜ. Removing 9 and 10 from Aᶜ leaves {6,7,8}. Equivalently, Aᶜ − Bᶜ = Aᶜ ∩ B. Therefore, option A is 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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