Let R be the relation on the set of all mathematicians that contains the ordered pair (a,b) if and only if "a" and "b" have written a published mathematical paper together.

a) Describe the relation R2.
b) Describe the relation R*.
c) The Erdos number of mathematician is 1 if this mathematician wrote a paper with the prolific Hungarian Paul Erdos, it is 2 if this mathematician did not write joint paper with Erdos but wrote a joint paper with someone who wrote a joint paper with Erdos, and so on (except that Erdos number of Erdos himself is 0). Give a definition of the Erdos number in terms of path in R.