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Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 19

For a finite universal set U, n(U)=64 and n(A)=3n(Aᶜ). What is the value of n(Aᶜ)?

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Answer and explanation

Correct answer: 16

Let n(Aᶜ)=x. The given relation says n(A)=3x. Because A and Aᶜ partition the finite universal set, their cardinalities add to n(U): n(A)+n(Aᶜ)=64. Substituting gives 3x+x=64, so 4x=64 and x=16. Therefore n(Aᶜ)=16. The value 48 is n(A), not the requested complement cardinality.

Tags

setscomplementcardinalityfinite setslinear equationComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

16

Why is this the correct answer?

Let n(Aᶜ)=x. The given relation says n(A)=3x. Because A and Aᶜ partition the finite universal set, their cardinalities add to n(U): n(A)+n(Aᶜ)=64. Substituting gives 3x+x=64, so 4x=64 and x=16. Therefore n(Aᶜ)=16. The value 48 is n(A), not the requested complement cardinality.

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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