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Class 10MathematicsSetsComplement of a Set and Its PropertiesHardLevel 10

If \(U=\{x\in\mathbb{Z}:-3\le x\le 8\}\), \(A=\{x\in U:x+1\ge4\}\), and \(B=\{x\in U:x<6\}\), what is \(A'\cup B'\)?

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Answer and explanation

Correct answer: \(\{-3,-2,-1,0,1,2,6,7,8\}\)

Within U, the condition \(x+1\ge4\) gives \(x\ge3\), so \(A=\{3,4,5,6,7,8\}\). Also, \(B=\{-3,-2,-1,0,1,2,3,4,5\}\). Therefore, \(A'\) contains \(-3,-2,-1,0,1,2\), while \(B'\) contains \(6,7,8\). Their union is \(\{-3,-2,-1,0,1,2,6,7,8\}\), option A.

Tags

setsintegerscomplementunioninequalitiesComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

\(\{-3,-2,-1,0,1,2,6,7,8\}\)

Why is this the correct answer?

Within U, the condition \(x+1\ge4\) gives \(x\ge3\), so \(A=\{3,4,5,6,7,8\}\). Also, \(B=\{-3,-2,-1,0,1,2,3,4,5\}\). Therefore, \(A'\) contains \(-3,-2,-1,0,1,2\), while \(B'\) contains \(6,7,8\). Their union is \(\{-3,-2,-1,0,1,2,6,7,8\}\), option A.

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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