Proving Set Theory Union in Cartesian Products

[rallycar18]

Homework Statement

Suppose A,B,C are sets. Prove that

A× (B U C)= (AxB) U (C x A)

 

[VeeEight]

Have you tried the usual inclusion both ways method?

 

[rallycar18]

Have you tried the usual inclusion both ways method?

I'm not familiar..

 

[TMM]

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

 

[statdad]

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 $x \in (A \times B) \cup (A \times C)$?