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Class 10MathematicsSetsPower Set and SubsetsHardLevel 10

In general, P(A) ∩ P(B) is equal to which of the following?

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Answer and explanation

Correct answer: P(A ∩ B)

An element of P(A) ∩ P(B) is a set that is a subset of both A and B. A set is a subset of both precisely when every one of its elements belongs to A ∩ B. Thus the common elements of the two power sets are exactly all subsets of A ∩ B, giving the identity P(A) ∩ P(B) = P(A ∩ B).

Tags

setspower-setset-identitiesintersectionPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

P(A ∩ B)

Why is this the correct answer?

An element of P(A) ∩ P(B) is a set that is a subset of both A and B. A set is a subset of both precisely when every one of its elements belongs to A ∩ B. Thus the common elements of the two power sets are exactly all subsets of A ∩ B, giving the identity P(A) ∩ P(B) = P(A ∩ B).

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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