If A∩B=∅, |A|=3, and |B|=4, what is |P(A)∩P(B)|?
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Answer and explanation
Correct answer: 1
A∩B=∅ means A and B have no common elements. Any set belonging to both P(A) and P(B) must be a subset of both A and B, so it must be a subset of A∩B. The only subset of the empty set is ∅. Hence P(A)∩P(B)={∅}, whose cardinality is 1, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
A∩B=∅ means A and B have no common elements. Any set belonging to both P(A) and P(B) must be a subset of both A and B, so it must be a subset of A∩B. The only subset of the empty set is ∅. Hence P(A)∩P(B)={∅}, whose cardinality is 1, so option B 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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