Proving Set Theory Union in Cartesian Products

rallycar18
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Homework Statement



Suppose A,B,C are sets. Prove that

A× (B U C)= (AxB) U (C x A)
 
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Have you tried the usual inclusion both ways method?
 
VeeEight said:
Have you tried the usual inclusion both ways method?

I'm not familiar..
 
Well if A is contained in B and B is contained in A, then A=B.
 
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)?
 

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