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Math Help - proof

  1. #1
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    proof

    Prove A U B= B U A

    I know this seems really obvious but I can't figure out how to formally prove it.
    Thanks!
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  2. #2
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    The disjunctive or is commutative.

    A or B is the same as B or A

    x \in A\; \vee \,x \in B is the same as x \in B\; \vee \,x \in A.
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  3. #3
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    I need to write up a proof of why that is true though
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  4. #4
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    The reason it is true is that or,  \vee , is commutative.
    That is the entire proof.
    \begin{gathered}<br />
  x \in \left( {A \cup B} \right)\; \Leftrightarrow x \in A \vee x \in B \hfill \\<br />
  x \in A \vee x \in B \equiv x \in B \vee x \in A \hfill \\<br />
  x \in B \vee x \in A \Leftrightarrow x \in \left( {B \cup A} \right) \hfill \\ <br />
\end{gathered}
    Last edited by Plato; September 10th 2010 at 03:27 PM.
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