transitive closure

The time complexity of computing the transitive closure of a binary relation on a set of elements is known to be:

Consider the binary relation: $$S = \left\{ {\left( {x,y} \right)|y = x + 1\,\,and\,\,x,y \in \left\{ {0,1,2,...} \right\}} \right\}$$ The reflexive transitive closure of $$S$$ is

The transitive closure of the relation $$\left\{ {\left( {1,2} \right)\left( {2,3} \right)\left( {3,4} \right)\left( {5,4} \right)} \right\}$$ on the set $$A = \left\{ {1,2,3,4,5}...