smaller(X,Y):- X
X>Y,write(Y),write(' is bigger then '),write(X),!;
write('They are equal').

Query -> ?smaller(3,5) : 3 is smaller then 5
Query -> ?smaller(8,5) : 8 is bigger then 5
Query -> ?smaller(5,5) : They are equal

2- Intersect relation

Intersect function uses an external function inside. Member function checks whether the first parameter is member of the given list or not.

Query -> member(3,[3,4,5]).

member(HM,[HM|TM]).
member(XM,[HM|TM]):- member(XM,TM).

and the intersect function gives you the result on LI variable. Try it.

intersect([ ],LI,[ ]).
intersect([HI|TI],LI,LI2):- member(HI,LI),intersect(TI,LI,LI3),LI2=[HI|LI3],!;intersect(TI,LI,LI2).

Query -> intersect([3,4],LI,[4,5]) : [4]

dog(rex).
dog(X):-parent(X,Y).
parent(goldie,rex).
parent(jack,rex).

Query -> ?dog(goldie) : YES
Query -> ?dog(jack) : YES

2- Sister relation

sister(X,Y):-girl(X),girl(Y),parent(X,Z),parent(Y,Z).
parent(sara,Maria).
parent(lili,Maria).
girl(lili).
girl(maria).

Query -> ?sister(lili,maria) : NO

3- Finds factorial of numbers

1!: 1 , 2!: 2×1, 3!: 3x2x1
Here you can see that we are able to say 3!: 3×2! instead of 3!:3x2x1 . Since i know what is 1! and 0! therefore i have limitation points for my program.

fact(0,1):-!.
fact(1,1):-!.
fact(N,F,F1) :- N1 is N-1, fact(N1,F1), F is N * F1.

4- Finds Fibonacci numbers

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,…

fib(0,0):-!.
fib(1,1):-!.
fib(X,L) :- X > 1, Y1 is X-1, Y2 is X-2, fib(Y1,F1), fib(Y2,F2), L is F1+F2.