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

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

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