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# Presenting symmetric relations on a set as graphs watch

1. '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?
2. (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.]
3. (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?
4. (Original post by Desmos)
Oh that makes sense. So then how is a graph defined mathematically?
Usual definition is that a graph is a pair where is a set of vertices and is our set of edges.

So for instance this graph:

Is defined by with:
and

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, .

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