Prolog Language Assignment:

Suppose we represent sets of (unsorted) integers as lists of integers with no duplicated elements. The universe will be the the integers from 1 to 20. Write Prolog rules for the following set operations (do NOT use any pre-defined predicates):

nodups(A,B): succeeds when A and B have the same items but B has no duplicates.

subset(A,B): succeeds when set A is a subset of set B.

union(A,B,C): succeeds when the union of sets A and B is C.

intersection(A,B,C): succeeds when the intersection of sets A and B is C .

difference(A,B,C): succeeds when the set difference of sets A and B is C.

complement(A,B): succeeds when the complement of the set A is B.

Here are few examples of queries and expected responses for nodups:

?- nodups([1,3,5,3], R).

R=[1,3,5]

?- nodups([1,3,5], R).

R=[1,3,5]

?- nodups([a,b,a,c,b], R).

R=[a,b,c]

?- nodups([a,b,a,c,b,a], R).

R=[a,b,c]

Here are few examples of the other queries and expected responses:

?- subset([1,3,5], [5,1,2,3]).

yes

?- subset([1,3,5], [3,1,5]).

yes

?- union([1,2,3], [2,3,7,9], U).

U=[1,2,3,7,9]

?- intersection([1,2,3], [2,3,7,9], I).

I=[2,3]

?- difference([1,2,3], [2,7,9,3], D).

D=[1]

SUBMISSION:

Submit two (ascii) files. The first file should contain your program which will include your facts and rules. The facts should appear first and should allow robust testing. The second file should contain 4 queries for each predicate (24 queries total). The queries should be different from the ones provided here, and should demonstrate different kinds of questions. This file should be readable, containing the queries on separate lines and explanations of them on separate lines.