Question

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

Answer 1

The power sets are given as,

P( A )=P( B )

P( A ) is the collection of all subsets of A, that is,

A∈P( A )

From the given condition,

P( A )=P( B )

A∈P( B )

Therefore,

A⊂B(1)

P( B ) is the collection of all subsets of B , that is,

B∈P( B )

From the given condition,

P( A )=P( B )

B∈P( A )

Therefore,

B⊂A(2)

From conditions (1) and (2),

A=B

Hence,

A=B