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Subjects
Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 19

If U = {1, 2, ..., 50}, A is the set of multiples of 2, and B is the set of multiples of 5, what is |A' ∩ B'|?

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Answer and explanation

Correct answer: 20

There are 25 multiples of 2 from 1 to 50 and 10 multiples of 5. The numbers counted in both sets are multiples of 10, of which there are 5. Thus |A ∪ B| = 25 + 10 − 5 = 30. By De Morgan's law, A' ∩ B' = (A ∪ B)', so |A' ∩ B'| = 50 − 30 = 20. Hence, option A is correct.

Tags

setscomplementscountingmultiplesComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

20

Why is this the correct answer?

There are 25 multiples of 2 from 1 to 50 and 10 multiples of 5. The numbers counted in both sets are multiples of 10, of which there are 5. Thus |A ∪ B| = 25 + 10 − 5 = 30. By De Morgan's law, A' ∩ B' = (A ∪ B)', so |A' ∩ B'| = 50 − 30 = 20. Hence, option A 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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