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Presenting symmetric relations on a set as graphs Watch

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    'One way of representing a symmetric relation on a set X visually is using a
    graph. This means drawing a point (or small blob) for each element of X
    and joining two of these if the corresponding elements are related.
    Draw each of the following symmetric relations as a graph.'

    This is an excerpt from my exercise sheet. So firstly, how would I plot the graph? What would the axes be? Also, if X were a set of sets, how would I plot its elements?
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    (Original post by Desmos)
    'One way of representing a symmetric relation on a set X visually is using a
    graph. This means drawing a point (or small blob) for each element of X
    and joining two of these if the corresponding elements are related.
    Draw each of the following symmetric relations as a graph.'

    This is an excerpt from my exercise sheet. So firstly, how would I plot the graph? What would thegg? Also, if X were a set of sets, how would I plot its elements?
    They don't mean a graph like y=x^2.

    Suppose X = {a, b, c, d, e}. You would literally write the letters "a", ..., "e" on a piece of paper (the positions don't matter, although some layouts might work out better than others), and draw lines between the letters that are related to each other.

    [You *might* want to draw circles round each object (letter) if you felt it made things clearer.]
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    (Original post by DFranklin)
    They don't mean a graph like y=x^2.
    Oh that makes sense. So then how is a graph defined mathematically?
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    (Original post by Desmos)
    Oh that makes sense. So then how is a graph defined mathematically?
    Usual definition is that a graph G is a pair G=(V,E) where V is a set of vertices and E \subseteq \left\{ \left\{ u, v \right\} | u,v\in V  \right\} is our set of edges.

    So for instance this graph:


    Is defined by G=(V,E) with:
    V=\left\{A,B, C\right\} and
    E=\left\{ \left\{A,B \right\}, \left\{B,C \right\}\right\}

    The nodes could be any set, it could be characters as here or numbers, etc. We usually consider set V to be finite.

    Sometimes we might want directed edges, in which case we define a digraph in the same way but instead, E \subseteq V\times V.
 
 
 
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