1. Given the relations

father(X,Y) X is the father of Y mother(X, Y) X is the mother of Y female(X) X is female male(X ) X is male

Define prolog relations for the following:

a. sibling b. sister c. grandson d. descendant

Provide some facts for the father, mother, male, and female predicates and then test the entire thing using Prolog.

2. Write a Prolog relation remove(E,L,R) that is true if R is the list which results from removing one instance of E from list L. The relation is false if E isnt a member of L.

What are all of the answers to the following queries?

ask remove(a,[b,a,d,a],R).

ask remove(E,[b,a,d,a],R).

ask remove(E,L,[b,a,d]).

ask remove(p(X),[a,p(a),p(p(a)),p(p(p(a)))],R).

3. Write a Prolog relation subsequence(L1,L2) that is true if list L1 contains a subset of the elements of L2 in the same order.

How many different proofs are there for each of the following queries?

ask subsequence([a,d],[b,a,d,a]).

ask subsequence([b,a],[b,a,d,a]).

ask subsequence([X,Y],[b,a,d,a]).

ask subsequence(S,[b,a,d,a]).

Explain why there are that many.

4. Write a Prolog relation that returns a list containing the union of the elements of two given lists.

5. Write another relation (anything you want) that does something not performed above. Explain what your relation does.