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Thread: Set Theory Transitivity Proof

  1. #1
    Member
    Joined
    Nov 2010
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    86

    Set Theory Transitivity Proof

    Hey all, how can we prove the following proposition about set theory?

    Let A,B,C be sets.

    If A=B and B=C then A=C


    Thanks!
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  2. #2
    Junior Member
    Joined
    Sep 2011
    Posts
    58

    Re: Set Theory Transitivity Proof

    Use the fact that $\displaystyle A=B \Leftrightarrow (A\subseteq B \text{ and } B\subseteq A)$

    Then start by letting some $\displaystyle x\in A$ and you can show that $\displaystyle x\in C$

    Then let some $\displaystyle y\in C$ and you can show $\displaystyle y\in A$
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