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## Homework Statement

Let A, B be non-empty sets, proof that A x B = B x A iff A = B

## Homework Equations

A x B = Cartesian Product

iff = if and only if

^ = and

## The Attempt at a Solution

Let (x,y) є A x B = B x A

iff (x,y) є (A X B) ^ (x,y) є (B x A)

iff (x є A ^ y є B) ^ (x є B ^ y є A)

iff (x є A ^ y є A) ^ (x є B ^ y є B)

iff (x,y) є A ^ (x,y) є B

iff (x,y) є A = B

Its that right?

Also, if one of the sets if empty, will the statement hold?

Thanks guys!