1. Find Transitive Closure

I am having problems understanding how to find the transitive closure of a Relation. Here is the problem:

Given U = {1, 2, 3, a, b} and the relation R on U is given by R = {(2,3), (3,2), (1,a)}

How does one find the transitive closure of R? I have found both the symmetric and reflexive closure, but don't know how to solve for the transitive.

2. Re: Find Transitive Closure

Originally Posted by aprilrocks92
I am having problems understanding how to find the transitive closure of a Relation. Here is the problem:

Given U = {1, 2, 3, a, b} and the relation R on U is given by R = {(2,3), (3,2), (1,a)}

How does one find the transitive closure of R? I have found both the symetric and reflexive closure, but don't know how to solve for the transitive.
Form $\tau=R\cup(R\circ R)$. Is $\tau$ transitive? Is it minimal?