Question

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

Answer 1

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 


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Answer 2

Answer:

Step-by-step explanation:

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.