Answer
The statement is true.
If A and B are any two sets and suppose x ∈ P(A ∩ B).
This means that x belongs to both A and B.
So, this can also be written as
x ∈ P(A ∩ B) = x ∈ P(A) and x ∈ P(B)
= x ∈ P (A) ∩ x ∈ P (B)
= x ∈ (P (A) ∩ P (B)) = P (A) ∩ P (B)
Work Step by Step
Steps:
1. Break down the function x ∈ P(A ∩ B) by the set intersection rule.
2. The statement is true if you can get P (A) ∩ P (B) by using set intersection rule.