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Subjects
Class 10MathematicsSetsComplement of a Set and Its PropertiesEasyLevel 19

If the universal set is U = [0, 12] and A = (3, 8], what is the complement Aᶜ of A with respect to U?

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Answer and explanation

Correct answer: [0, 3] ∪ (8, 12]

The complement Aᶜ contains all elements of the universal set U that are not in A. Since A = (3, 8], the number 3 is excluded from A and therefore belongs to Aᶜ. The number 8 is included in A, so it must be excluded from the complement. Thus, within U = [0, 12], the complement is [0, 3] ∪ (8, 12].

Tags

setscomplementintervalsuniversal setComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

[0, 3] ∪ (8, 12]

Why is this the correct answer?

The complement Aᶜ contains all elements of the universal set U that are not in A. Since A = (3, 8], the number 3 is excluded from A and therefore belongs to Aᶜ. The number 8 is included in A, so it must be excluded from the complement. Thus, within U = [0, 12], the complement is [0, 3] ∪ (8, 12].

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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