Assume that P (A) = P (B). Show that A = B.
Let P(A) = P(B)
To show: A = B
Let x ∈ A
A ∈ P(A) = P(B)
∴ x ∈ C, for some C ∈ P(B)
Now, C ⊂ B
∴ x ∈ B
∴ A ⊂ B
Similarly, B ⊂ A
∴ A = B
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