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Exercice 2)

1) Vrai.

2) Faux. 
Exemple: 

programme:  

p(X):-fail. 
p(a).

requete: p(X).

3)Vrai.

4) Faux.

Exemple:

programme:

p(X):-(X=A;X=B)


Exercice 3) 

1)
insert(X,[],[X]).
insert(X,[Y|Z],[X,Y|Z]):-X=<Y.
insert(X,[Y|Z],[Y|T]):-X>Y,insert(X,Z,T).

trii([],[]).
trii([X|T],Y):-trii(T,Z),insert(X,Z,Y).

2)
split([],[],[]).
split([X],[X],[]).
split([X,Y|T],[X|L],[Y|S]):-split(T,L,S).


merge([],X,X).
merge(X,[],X).
merge([X|T],[Y|S],[X|R]):-X=<Y,merge(T,[Y|S],R).
merge([X|T],[Y|S],[Y|R]):-X>Y,merge([X|T],S,R).


trif([],[]).
trif(X,Z):-split(X,L,S), trif(L,M),trif(S,N),merge(M,N,Z).

3)
it([],[]).
it([X],[X]).
it([X,Y|Z],[X|T]):-X=<Y, it([Y|Z],T).
it([X,Y|Z],[Y|T]):-X>Y, it([X|Z],T).

trib(X,Y):-it(X,T),(X==T-> Y=T; trib(T,Y))

Exercice 4)

1) Une liste d'entiers.

2)

between(P,Q,P):-P<Q.
between(P,Q,R):-P<Q, S is P+1, between(S,Q,R).

move([N|L],[N1,N2|L]):-between(1,N,N1),between(1,N,N2), N=:=N1+N2,
N1=\=N2.

move([N|L],[N|T]):-move(L,T).


3)

gagne(P):-move(P,Q), not(gagne(Q)).