Proving Set Theory Union in Cartesian Products

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Homework Help Overview

The discussion revolves around proving a property of sets involving Cartesian products and unions. The original poster presents a statement involving sets A, B, and C, and seeks to establish the equality between the Cartesian product of A with the union of B and C, and the union of the Cartesian products of A with B and A with C.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the inclusion method for proving set equalities. There is a suggestion to consider the definitions of Cartesian products and unions to analyze elements within the sets.

Discussion Status

The discussion is ongoing, with participants exploring different methods to approach the proof. Some guidance has been offered regarding the definitions involved, but no consensus has been reached on a specific method or solution.

Contextual Notes

There is a mention of familiarity with the inclusion method, indicating varying levels of understanding among participants. The original poster's assumptions about the sets and their relationships have not been fully clarified.

rallycar18
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Homework Statement



Suppose A,B,C are sets. Prove that

A× (B U C)= (AxB) U (C x A)
 
Last edited:
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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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