Problem

1. Suppose you are given a description of a map in terms of the relation from to. From to (a, b) means that one can directly reach point b from point a. Assume that from any point X one cannot return to the same point by applying the closure of relation from to (i.e., the map contains no cycles). A special point, called exit, represents the exit from the map. Write a PROLOG program to check if, given a starting point, one can reach exit.

2. Referring to the previous exercise, write a PROLOG predicate to check if the assumption that the map contains no cycles hold; i.e., from any point X one cannot return to the same point by applying the closure of relation from to.