#### 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)

∴ *x *∈ C, for some C ∈ P(B)

Now, C ⊂ B

∴ *x* ∈ B

∴ A ⊂ B

Similarly, B ⊂ A

∴ A = B

Is there an error in this question or solution?

Solution Assume that P (A) = P (B). Show that a = B. Concept: Equal Sets.