Write a short implementation for each of the following predicates. (i) unify/2 is true if and only

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Write a short implementation for each of the following predicates. (i) unify/2 is true if and only if its two arguments can be unified. [1 mark] (ii) fail/0 is never true. [1 mark] (iii) numequal/2 is true if and only if its arguments, interpreted as numerical expressions (assume integer values and no use of division), are numerically equal. For example, numequal(1+3,2+2) is true. [1 mark] (iv) member/2 is true if and only if its first argument is within the list that is its second argument. [1 mark] (b) Given the following code, list all solutions, in order, for the query c(X,Y,Z). a(1). a(2). b(a). c(A,B,C) :- a(A),d(B,C). c(A,B,C) :- b(A),d(B,C). d(B,C) :- a(B),!,a(C). d(B,_) :- b(B). [4 marks] (c) The recursive clause of a bubblesort predicate is reproduced below (assume that append/3 is defined already). Define two different base clauses for this predicate, one of which should use a green cut. When the first argument is unified with a list containing only integers, both of your answers should produce no additional solutions on backtracking. Explain how your complete bubblesort predicate works, including the purpose of the red cut. bubblesort(X,Y) :- append(A,[H1,H2|B],X), H1 > H2, !, append(A,[H2,H1|B],X1), bubblesort(X1,Y). [6 marks] (d) The power set of a set S is the set of all subsets of S. We will represent sets using lists (ignore list order and assume no duplicates). Write a predicate ps(+S,-PS) that unifies PS with the power set of S, and explain how it works. Include the code for all predicates that you use.

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