If |A ∩ B| = 4, what is |P(A) ∩ P(B)|?
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Answer and explanation
Correct answer: 16
A set belongs to both P(A) and P(B) exactly when it is a subset of both A and B. Being a subset of both means that it contains only elements common to A and B. Hence, P(A) ∩ P(B) = P(A ∩ B). Since |A ∩ B| = 4, its power set has 2⁴ = 16 members. Therefore, option C is correct.
Frequently asked questions
What is the correct answer to this question?
16
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. Being a subset of both means that it contains only elements common to A and B. Hence, P(A) ∩ P(B) = P(A ∩ B). Since |A ∩ B| = 4, its power set has 2⁴ = 16 members. Therefore, 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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