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Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 19

If U has n(U)=54 and a set A satisfies n(Aᶜ)=2n(A), what is the value of n(A)?

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Answer and explanation

Correct answer: 18

Let n(A)=x. Then the condition n(Aᶜ)=2n(A) gives n(Aᶜ)=2x. A set and its complement partition U, so n(A)+n(Aᶜ)=n(U). Hence x+2x=54, or 3x=54. Dividing by 3 gives x=18. Therefore n(A)=18, while the complement has 36 elements. This also confirms that the two cardinalities add to 54.

Tags

setscomplementcardinalityalgebraic equationsfinite universal setComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

18

Why is this the correct answer?

Let n(A)=x. Then the condition n(Aᶜ)=2n(A) gives n(Aᶜ)=2x. A set and its complement partition U, so n(A)+n(Aᶜ)=n(U). Hence x+2x=54, or 3x=54. Dividing by 3 gives x=18. Therefore n(A)=18, while the complement has 36 elements. This also confirms that the two cardinalities add to 54.

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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