*** 1
?- parent(john, X). 
X = mary

?- parent(X, john). 
X = paul

?- parent(parent, X), parent(X, Y), parent(Y,Z). 
no

*** 2.a
sum(A3,A2,A1,B3,B2,B1,S4,S3,S2,S1) :-
	halfadder(A1,B1,C1,S1),
	fulladder(A2,B2,C1,S2,C2),
	fulladder(A3,B3,C2,S3,S4).

*** 2.b
% first solution
% calculates S=A-B (A in 4 bits, B in 3 bits, S in 3 bits)
% doesn't work when the result takes 4 bits
sub4(A4,A3,A2,A1,B3,B2,B1,S3,S2,S1) :-
	sum(B3,B2,B1,S3,S2,S1,A4,A3,A2,A1).

% second solution
% calculates S=A-B (A,B,S all in 3 bits)
% doesn't work when the result takes 4 bits
sub3(A3,A2,A1,B3,B2,B1,S3,S2,S1) :-
	sum(B3,B2,B1,S3,S2,S1,0,A3,A2,A1).

*** 3
grandparent(X,Y):-parent(X,Z),parent(Z,Y).


*** 4
T_P^0 = {}
T_P^1 = T_P({}) = set of facts defining the truth tables of and, or, eor, not
T_P^2 = T_P(T_P^1) = T_P^1 union the set of facts defining the truth tables of halfadder and fulladder
T_P^3 = T_P(T_P^2) = T_P^2 union the set of facts defining the truth tables of sum
T_P^4 = T_P(T_P^3) = T_P^3 union the set of facts defining the truth tables of sub3 and sub4
T_P^5 = T_P(T_P^4) = T_P^4
this is a fixpoint and thus is the least Herbrand model