Hi,

The question is as follows:

The transitive closure of a relation R on S x S is another relation on S x S called Tr(R) such that $\displaystyle (s,t) \in Tr(R)$ iif there exists a sequence $\displaystyle s=s_1, s_2, s_3, \ldots, s_n = t$ such that $\displaystyle (s_i, s_{i+1}) \in R$ for each $\displaystyle i$.

a) What is the transitive closure of the successor relation? (Defined previously on N x N as: $\displaystyle \lbrace (m, n) | m = n+1\rbrace$).

b) What is the transitive closure of the > relation?

The book introduced this concept right in this exercise question without showing any examples. I'm a bit stuck as to how I might interpret this somewhat complex definition [of a transitive closure] and derive the solution.