# Homework Help: Set theory union question

1. Jun 5, 2010

### rallycar18

1. The problem statement, all variables and given/known data

Suppose A,B,C are sets. Prove that

A× (B U C)= (AxB) U (C x A)

Last edited: Jun 6, 2010
2. Jun 5, 2010

### VeeEight

Have you tried the usual inclusion both ways method?

3. Jun 5, 2010

### rallycar18

I'm not familiar..

4. Jun 5, 2010

### TMM

Well if A is contained in B and B is contained in A, then A=B.

5. Jun 6, 2010

assume $x \in A \times (B \cup C)$. Think about the definitions of Cartesian product and union: what can you conclude about the element $x$; can you use this information to show $x \in (A \times B) \cup (A \times C)$?