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Class 10MathematicsSetsComplement of a Set and Its PropertiesEasyLevel 19

If \(U=\{x:x\in\mathbb{Z},0\le x\le15\}\) and \(A=\{x:x\text{ is prime}\}\), which element must be in \(A'\)?

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Answer and explanation

Correct answer: 9

The universal set contains the integers from 0 through 15. Among the options, 2, 3, and 13 are prime, so they belong to A. The number 9 is composite because \(9=3\times3\), and it is in U but not in A. Therefore, 9 belongs to the complement \(A'=U\setminus A\), making C correct.

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setscomplementprime numbersintegersComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

9

Why is this the correct answer?

The universal set contains the integers from 0 through 15. Among the options, 2, 3, and 13 are prime, so they belong to A. The number 9 is composite because \(9=3\times3\), and it is in U but not in A. Therefore, 9 belongs to the complement \(A'=U\setminus A\), making C 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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