If |A|=4, |B|=5, and |A∩B|=2, what is |P(A)∩P(B)|?
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Answer and explanation
Correct answer: 4
A set belongs to both P(A) and P(B) exactly when it is a subset of both A and B. Such sets are precisely the subsets of A∩B, so P(A)∩P(B)=P(A∩B). Since |A∩B|=2, its power set has 2^2=4 members. Therefore option B is correct; the separate sizes of A and B are not needed.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
A set belongs to both P(A) and P(B) exactly when it is a subset of both A and B. Such sets are precisely the subsets of A∩B, so P(A)∩P(B)=P(A∩B). Since |A∩B|=2, its power set has 2^2=4 members. Therefore option B is correct; the separate sizes of A and B are not needed.
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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