Consider the following Prolog program:

edge(a, b).

edge(c, d).

edge(a, c).

edge(c, b).

edge(X, Y) :- edge(Y, X).

path(X, X).

path(X, Y) :- edge(Z, Y),

path(X, Z).

Note that this program is nearly identical to one presented in lecture except for the inclusion of the extra rule: edge(X, Y) :- edge(Y, X).

The intent is that, with this additional rule, the program should model an undirected (as opposed to directed) graph.

(a) Execute the query: ?- edge(a,b). What response do you get?

(b) Execute the query ?- edge(b,a). What response do you get?

(c) Execute the query ?- edge(a, d). What response do you get? And why?