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Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 20

If U = {1, 2, …, 49}, A = {x : x is a perfect square}, and B = {x : x is odd}, what is |A′ ∩ B|?

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Answer and explanation

Correct answer: 21

There are 25 odd integers from 1 through 49. The perfect squares in this universe are 1, 4, 9, 16, 25, 36, and 49; the odd ones among them are 1, 9, 25, and 49, four numbers. A′ ∩ B consists of odd numbers that are not perfect squares, so its cardinality is 25 − 4 = 21. Therefore, option B is correct.

Tags

setscomplementperfect squaresodd numbersComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

21

Why is this the correct answer?

There are 25 odd integers from 1 through 49. The perfect squares in this universe are 1, 4, 9, 16, 25, 36, and 49; the odd ones among them are 1, 9, 25, and 49, four numbers. A′ ∩ B consists of odd numbers that are not perfect squares, so its cardinality is 25 − 4 = 21. Therefore, option B is correct.

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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