CSCI 320, Homework 10, Logic programming in Prolog

Collaboration: You may discuss the assignment with peers, but you must do your ownwork. It is not OK to copy or share solutions, or look for solutions on the Internet. If you dorun into a solution, you may use it but you must acknowledge the find and you may notshare it with others. It is OK to discuss how to use the prolog editor and prolog system inthe lab, which is now working . Log in using your Woosters account and put input into theeditor window – issue a “consult” command when you want your code to be executed. Theeditor comes with a manual and automatically finds the prolog interpreter.1‐4: Exercises 1‐4, Sebesta, page 736. Use the following names for the main rules in each:a‐ maximum, 2 – intersection, 3‐ union, 4 –last5‐ Define the nonMember relationship, nonMember(X, List) that does not use the memberrelationship. nonMember returns true if element X is not in list List.6‐ Write a program call fib, such that fib(n, fn) is true if and only if fn is the nth numberin the Fibonacci sequence. Recall that fib0 =1, fib1 = 1 and for all n1, fibn = fibn‐1 + fibn‐2.7‐ Given a list of the form [item(name1, price1), item(name2, price2),…, item(namek,pricek)].a. Write rule(s) called cost(L, Name, Price) which given a list L (as above) and Name,gives the Price of that item.b. Can this rule be run backward? That is, what happens when you provide the list Land Price, but not the Name?c. Write rule(s) called listcost(L, Names, Price) where L is a list as above, Names isa list of names of items, and Price is to be computed as the total cost of all the itemsin list Names. Can this be run backward?8 – Consider a graph represented as a sequence of edges between vertices such as below(written more than one per line to save space here):edge(a, b). edge(a, f). edge(b, c). edge(b, f).edge(c, a). edge(c, f). edge(d, e). edge(e, a).edge(e, c).Write rule(s) that give a path from a start vertex to a finish vertex, path(Start,Finish). The path that may not visit any vertex more than once, other than possibly thestart vertex, which could also be the finish vertex. For the graph above, one path from a to fwould be a – b – f, another is a‐f, but the following a – b – c –a – f is not considered a pathfor this problem.All code and non‐code answers must appear in a single file, which is to be uploaded toOAKS. For non‐code answers, include them as comments (‘%’ at start of line). Make surethat documentation includes your name and a label in terms of problem number and letter,if appropriate, for each problem. Make sure that they are in order in the file uploaded.