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Class 10MathematicsSetsPower Set and SubsetsEasyLevel 9

If U = {1, 2, 3, 4, 5, 6} and A = {1, 3, 6}, how many elements are in the power set P(A′) of the complement A′?

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Answer and explanation

Correct answer: 8

First calculate the complement relative to U: A′ = U − A = {2, 4, 5}. Thus A′ has three elements. A set with n elements has 2ⁿ subsets, so its power set has 2³ = 8 elements. Therefore, P(A′) contains 8 elements. The answer is not 16 because the complement has three, not four, elements.

Tags

setspower_setcomplementexponentsPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

8

Why is this the correct answer?

First calculate the complement relative to U: A′ = U − A = {2, 4, 5}. Thus A′ has three elements. A set with n elements has 2ⁿ subsets, so its power set has 2³ = 8 elements. Therefore, P(A′) contains 8 elements. The answer is not 16 because the complement has three, not four, elements.

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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