# Transitive Closure

Let:

- $X$ be the set of elements
- $\mathcal R$ be the set of relations
- $\mathcal R^2$ be the set of relations which can be reached from two hops of relations in $\mathcal R$
- For example,
`(a,c)`

is reached by going through`(a,b) -> (b,c)`

- For example,
- $\mathcal R^*$ is the entire transitive closure over $\mathcal R$