Assume that P (A) = P (B). Show that A = B.
Question:

Assume that P (A) = P (B). Show that A = B.

Solution:

Let P(A) = P(B)

To show: A = B

Let x ∈ A

A ∈ P(A) = P(B)

∴ ∈ C, for some C ∈ P(B)

Now, C ⊂ B

∴ x ∈ B

∴ A ⊂ B

Similarly, B ⊂ A

∴ A = B

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