transitive closures

. Note, take the nodes in A in the order given.

Use Warshall’s Algorithm to determine the transitive closure of R.

Draw the digraph of the transitive closure of R and use the digraph to
explain the idea of connectivity. Is this graph connected? What does
this mean?

*Note there is a version of Warshall’s Algorithm given in the my book,
that illustrates this but I’m having trouble applying it to this
problem.

Here’s the example I’m trying to follow:

Find the zero-one matrix of the transitive closure of the relation to R
where

.

Solution: From Theorem 3, (Let MR be the zero-one matrix of the
relation R on a set with n elements. Then the zero-one matrix of the
transitive closure R* is

M[n]R) it follows that the zero-one matrix of R* is:

M[3]R .

Since



it follows that