" Let X be a set of at least two people. We will ask each person in X to write down the nameof a person in X other than themself. Let R be the relation {a, b : as chosen name is b}.Suppose we start with a given person a, move to the person that a wrote down, then to theperson that they wrote down, and so forth until we reach a given person b. Let S be therelation {a, b: Starting from a, we eventually reach b by this process}.

(a) If from a, we reach a again before nding b, explain why we will never reach b."

"(b) If a, b is not in S, when can we give up on the process? Will we denitely reach a?

(c) (uses Java) If the elements of X are represented by the integers {0, . . . , n 1} for somen, and the relation R is given by a two-dimensional boolean array, write a method thatwill test whether a given pair is a member of S"