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Class 10MathematicsSetsPower Set and SubsetsHardLevel 10

If U = {1,2,3,4,5,6,7,8}, A = {1,2,3,4}, and B = {3,4,5,6}, what is |𝒫((A ∩ B)′)|?

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Answer and explanation

Correct answer: 64

First find the intersection: A ∩ B = {3,4}, which has 2 elements. The complement is taken relative to U, so (A ∩ B)′ = U − {3,4} = {1,2,5,6,7,8}. This complement has 6 elements. The number of subsets of any six-element set is 2^6 = 64, including the empty subset. Hence |𝒫((A ∩ B)′)| = 64, making option C correct.

Tags

setsintersectioncomplementpower setfinite setsPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

64

Why is this the correct answer?

First find the intersection: A ∩ B = {3,4}, which has 2 elements. The complement is taken relative to U, so (A ∩ B)′ = U − {3,4} = {1,2,5,6,7,8}. This complement has 6 elements. The number of subsets of any six-element set is 2^6 = 64, including the empty subset. Hence |𝒫((A ∩ B)′)| = 64, making option C 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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