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Subjects
Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 19

If the universal set is U = ℝ, A = (−∞, 0] and B = [2, ∞), what is A′ ∩ B′?

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Answer and explanation

Correct answer: (0, 2)

Complements are taken relative to ℝ. Since A includes all real numbers up to and including 0, A′ = (0, ∞). Since B includes all real numbers from 2 onward, including 2, B′ = (−∞, 2). Their intersection is therefore the real interval (0, 2). Both endpoints are excluded: 0 is in A and 2 is in B.

Tags

setscomplementintervalsintersectionComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

(0, 2)

Why is this the correct answer?

Complements are taken relative to ℝ. Since A includes all real numbers up to and including 0, A′ = (0, ∞). Since B includes all real numbers from 2 onward, including 2, B′ = (−∞, 2). Their intersection is therefore the real interval (0, 2). Both endpoints are excluded: 0 is in A and 2 is in B.

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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