Question

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

Answer 1

Answer :-

To show :-

A = B

According to the question,

P (A) = P (B)

Let x be any element of set A,

x ∈ A

Since, P (A) is the power set of set A, it has all the subsets of set A.

A ∈ P (A) = P (B)

Let C be an element of set B

For any C ∈ P (B),

We have, x ∈ C

C ⊂ B

∴ x ∈ B

∴ A ⊂ B

Similarly, we have:

B ⊂ A

So, we get,

If A ⊂ B and B ⊂ A

∴ A = B