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Class 10MathematicsSetsComplement of a Set and Its PropertiesEasyLevel 20

Let the universal set be U = [-2, 3] and A = (-1, 2]. What is the complement Aᶜ of A with respect to U?

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Answer and explanation

Correct answer: [-2, -1] ∪ (2, 3]

The complement Aᶜ consists of the elements in U that are not in A. Because A = (-1, 2] excludes -1, the point -1 belongs to the complement. Because A includes 2, the complement must exclude 2. Thus the remaining portions of U are [-2, -1] and (2, 3], so Aᶜ = [-2, -1] ∪ (2, 3].

Tags

setscomplementintervalsendpoint notationComplement of a Set and Its PropertiesMathematicsClass 10Class 10 MCQ

Frequently asked questions

What is the correct answer to this question?

[-2, -1] ∪ (2, 3]

Why is this the correct answer?

The complement Aᶜ consists of the elements in U that are not in A. Because A = (-1, 2] excludes -1, the point -1 belongs to the complement. Because A includes 2, the complement must exclude 2. Thus the remaining portions of U are [-2, -1] and (2, 3], so Aᶜ = [-2, -1] ∪ (2, 3].

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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