What is a transitive closure relation in discrete mathematics?

Answer 1

To get a feel for the concept of transistive closure, let's start with an example. Suppose the relation R is "likes" and the set is the people in a high school class. That is, for people in the class labeled a and b, "a R b" means "a likes b". Suppose a likes b and b likes c. Generally, this does not mean that a likes c. The transitive closure of R is a new relation R', where "a R' c" means "a likes c or a likes someone who likes c".

So, formally, for any relation R on a set S, the transitive closure of R, denoted by R', is the set of all pairs (a, c) where (a, b) is in R and (b, c) is R. (Note that R' includes all the pairs (a, b) in R.)