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Math Help - Equivalence Relations - HELP!!!

  1. #1
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    Exclamation Equivalence Relations - HELP!!!

    Ok so i'm a little stuck on how to prove this..

    Consider the set of points (x,y) in the plane (real numbers)^2. Define a relation R(subset 2) on the set as follows:

    (x1,y1)R(subset 2)(x2,y2) whenever x1y1=x2y2

    Prove that R(subset 2) is an equivalence relation.

    Any help would be greatly appreciated. I know i need to prove that it is reflexive, symmetric and transitive but i'm not sure on how to go about it.
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  2. #2
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    \begin{gathered}<br />
\left( {x,y} \right)R\left( {x,y} \right) \Leftrightarrow xy = xy\,\,\text{reflexive} \hfill \\<br />
\left( {x,y} \right)R\left( {y,x} \right) \Leftrightarrow xy = yx\,\,\text{symetric}\hfill \\ \end{gathered}


     <br />
\begin{gathered}<br />
\left( {x,y} \right)R\left( {u,v} \right)\,\& \,\left( {u,v} \right)R\left( {w,z} \right) \hfill \\<br />
xy = uv\,\& \,uv = wz \hfill \\<br />
xy = wz \hfill \\<br />
\left( {x,y} \right)R\left( {w,z} \right) \hfill \\ <br />
\end{gathered} <br /> <br />
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