use Prolog programming

Design two predicates path/2 and cycle/1 that determine structures within a graph whose directed edges are encoded with given instances of edge/2. For example, path(x,y) should evaluate to true if a path exists from vertex x to vertex y, and false otherwise. And cycle(x) should evaluate to true if a cycle exists which includes vertex x.

Note: All edges are directional. Note: Your solution should avoid infinite recursion.

Note: The Knowledge Base of edges below is for example only.

You are just responsible for the definitions of path/2 and cycle/1. The Knowledge Base edges used for grading will be different.

Example:-

Knowledge Base

edge(a,b).

edge(b,c).

edge(c,d).

edge(d,a).

edge(d,e).

edge(b,a).

?- path(b,d)

true.

?- path(e,b).

false.

?- path(c,a).

true.

?- cycle(b).

true.

?- cycle(e).

false.