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Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 9

If U = ℝ and A = (−∞, 2], what is A′?

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Answer and explanation

Correct answer: (2,∞)

The complement is taken with respect to U = ℝ. The interval A = (−∞,2] contains every real number less than 2 and also 2 itself. Consequently, the complement contains exactly the real numbers greater than 2. Since 2 already belongs to A, it must not be included in A′, so the correct interval is (2,∞).

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setscomplementintervalsreal-numbersComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

(2,∞)

Why is this the correct answer?

The complement is taken with respect to U = ℝ. The interval A = (−∞,2] contains every real number less than 2 and also 2 itself. Consequently, the complement contains exactly the real numbers greater than 2. Since 2 already belongs to A, it must not be included in A′, so the correct interval is (2,∞).

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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