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Subjects
Class 10MathematicsSetsPower Set and SubsetsHardLevel 9

Let U = {x ∈ N : 1 ≤ x ≤ 20} and A = {x ∈ U : x is prime}. How many non-empty subsets does A' have?

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Answer and explanation

Correct answer: 4095

The primes from 1 through 20 are 2, 3, 5, 7, 11, 13, 17, and 19, so A has 8 elements. Since U has 20 elements, the complement A' has 20 − 8 = 12 elements. Its power set contains 2^12 = 4096 subsets, including the empty set. Therefore the number of non-empty subsets is 4096 − 1 = 4095, so option B is correct.

Tags

setscomplementprime-numbersnon-empty-subsetsPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

4095

Why is this the correct answer?

The primes from 1 through 20 are 2, 3, 5, 7, 11, 13, 17, and 19, so A has 8 elements. Since U has 20 elements, the complement A' has 20 − 8 = 12 elements. Its power set contains 2^12 = 4096 subsets, including the empty set. Therefore the number of non-empty subsets is 4096 − 1 = 4095, so option B 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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