TITLE: How to visually represent a relation made up of relations?
QUESTION [0 upvotes]: If 
$$R_1 ≡ \{(a,a), (a,b), (b,c),(c,a)\}$$
$$R_2 ≡ \{(a,1), (a,2), (b,3),(c,3)\}$$
$$R_3 ≡ \{(a,1), (a,2), (b,3),(c,3)\}$$
Using set notation and actual lines to connect the pairs, I want to show the relation 
$$R_4 ≡ R_1 R_2 R_3^{-1}$$
I think the set notation would be 
$$R_4 = \{(a,a), (a,b), (a,c),(b,b),(b,c),(c,a),(c,b)\}$$
And I have no idea how to insert the oval shape think to show the process visually, so if anybody can do that it would be of great help.

REPLY [0 votes]: You can visualise a binary relation $R$ over a set $A$ as a directed graph $G_R$ whose vertices are the elements of $A$ and whose edges correspond to the elements of the relation: If $(a,b) \in R$, then there is an edge from $a$ to $b$ in $G_R$.
Now use distinct colours for the edges corresponding to the three relations and a fourth colour to represent $R_4$.
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