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Assume that P (A) = P (B). 

Show that A = B. 

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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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