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Class 10MathematicsSetsPower Set and SubsetsHardLevel 9

If U = {1,2,3,4,5,6,7,8,9}, A = {1,3,5,7,9}, and B = {2,3,5,8}, what is |P((A − B)′)|?

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Answer and explanation

Correct answer: 64

First calculate the difference: A − B = {1,7,9}, because 3 and 5 belong to both A and B. The prime symbol means complement relative to U. Hence (A − B)′ = U − {1,7,9} = {2,3,4,5,6,8}, which has 6 elements. Its power set therefore has 2⁶ = 64 members. Thus option C is correct.

Tags

setsdifferencecomplementpower-setuniversal-setPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

64

Why is this the correct answer?

First calculate the difference: A − B = {1,7,9}, because 3 and 5 belong to both A and B. The prime symbol means complement relative to U. Hence (A − B)′ = U − {1,7,9} = {2,3,4,5,6,8}, which has 6 elements. Its power set therefore has 2⁶ = 64 members. Thus option C 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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