/* ----------------------- */
/*  Operatii cu multimi  */
/* ----------------------- */

/*  member  */
/*  member(X,List) -> X este membru in List  */
member(X,[X|Y]).
member(X,[Y|Z]) :- member(X,Z).

/*  subset  */
/*  subset(X,Y) -> X este o submultime a lui Y  */
subset([A|X],Y) :- member(A,Y), subset(X,Y).
subset([],Y).

/*  disjoint  */
/*  disjoint(X,Y) -> X este disjuncta fata de Y  */
disjoint(X,Y) :- not( (member(Z,X),member(Z,Y)) ).

/*  intersection  */
/*  intersection(X,Y,Z) -> Z este intersectia lui X cu Y  */
intersection([],X,[]).
intersection([X|R],Y,[X|Z]) :- member(X,Y), !, intersection(R,Y,Z).
intersection([X|R],Y,Z) :- intersection(R,Y,Z).

/*  union  */
/*  union(X,Y,Z) -> Z este reuniunea lui X si Y  */
union([],X,X).
union([X|R],Y,Z) :- member(X,Y), !, union(R,Y,Z).
union([X|R],Y,[X|Z]) :- union(R,Y,Z).

/* --------- */
/*  Teste  */
/* --------- */
?- trace.
?- member(i,[a,e,i,o,u]).
?- member(t,[a,e,i,o,u]).
?- member(X,[a,e,i,o,u]).

/* ?- subset(X,[a,b,c,d,e]). */
?- subset([a,f],[a,b,c,d,e]).
?- subset([a,d],[a,b,c,d,e]).

?- disjoint([a,e,i],[o,u]).
?- disjoint([s,t,p],[t,x]).

?- intersection([a,e,i],[o,u],L).
?- intersection([s,u,m],[r,s,m],L).

?- union([a,e,i],[o,u],L).
?- union([x,y,z],[w,z],L).