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

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

Answer
Every set is a member of power set so that, A ∈ P(A)
Given that P (A) = P (B) So that
A ∈ P(B)
A is a element of power set of B so that,
A ⊂ B ... (1)
Similarly we can prove that
B ⊂ A ... (2)
From equation (1) and (2) we get, A = B