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Class 10MathematicsSetsPower Set and SubsetsHardLevel 10

Let U = {1, 2, 3, ..., 30}, and let A be the set of numbers divisible by 2 or 3. What is |A′|?

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Answer and explanation

Correct answer: 10

There are 15 numbers from 1 to 30 divisible by 2 and 10 divisible by 3. Numbers divisible by both 2 and 3, that is, divisible by 6, are counted twice; there are 5 of them. By inclusion–exclusion, |A| = 15 + 10 − 5 = 20. Since U has 30 elements, the complement has |A′| = 30 − 20 = 10 elements. Hence option A is correct.

Tags

setscomplementinclusion-exclusiondivisibilityuniversal setPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

10

Why is this the correct answer?

There are 15 numbers from 1 to 30 divisible by 2 and 10 divisible by 3. Numbers divisible by both 2 and 3, that is, divisible by 6, are counted twice; there are 5 of them. By inclusion–exclusion, |A| = 15 + 10 − 5 = 20. Since U has 30 elements, the complement has |A′| = 30 − 20 = 10 elements. Hence option A is correct.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.

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