The tabular and graphical representations of relations $R$ and $S$ have been provided:

1. Relation $R$: Displays pairs where $a < b$.
2. Relation $S$: Displays pairs where $a + b$ is divisible by 3.

Next, I'll calculate the derived relations as specified in part (b), including $S^{-1}$, $\overline{S}$, $\overline{R}$, $S^{-1} \circ S$, and $S \circ S$.

If you have questions about the tables or graphs, or if you want further details on the interpretation, let me know!

Here are some further questions to deepen understanding:

1. What properties do relations $R$ and $S$ exhibit (e.g., reflexive, symmetric, transitive)?
2. How do inverse and complement operations affect the properties of a relation?
3. What is the significance of the composition of relations, particularly in this context?
4. Can we generalize the results for larger subsets beyond $\{0, \dots, 5\}$?
5. How would the graphical representations change if we used a larger or different subset?

Tip: In relations, composition can reveal how connections between elements propagate, providing insight into the structure of interconnected sets.