Let us go back to the network we have been studying in the previous few homework assignments. Only, this time, it is a social network involving people who are connected by a friend relation- ship, represented below: as Prolog code on the left, and a graphical representation on the right. Note that this friend relationship is symmetric, since, on the left, for each pair X, Y of people, if friend(X,Y), then friend(Y,X), and in the graphical representation on the right, the “edges” do not have direction. friend(abi, bea). friend(abi, cory). friend(bea, cory). friend(bea, dina). friend(cory, dina). friend(dina, eva). friend(dina, fei). friend(eva, fei). friend(fei, gil). friend(bea, abi). friend(cory, abi). friend(cory, bea). friend(dina, bea). friend(dina, cory). friend(eva, dina). friend(fei, dina). friend(fei, eva). friend(gil, fei). Write the Prolog predicate friend of a friend(X,Y) which is true when X has a friend who is a friend of Y. Note: that this does not preclude X from also being a friend of Y, but it does preclude X from being a friend of a friend of itself, i.e., friend of a friend(X,X) should be false.

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Heuristic System

The term heuristic is derived from the Greek word heurisko, which means “I find, discover”. Heuristics can be mental shortcuts or approaches designed from previous experiences. The main aim of the heuristic approach is to find a good enough solution to solve the problem. Test and mistake, rule of thumb, or an educated estimate are all examples of heuristics. These methods are sufficient for achieving an immediate, brief aim. When a heuristic is used in practice, it works as predicted. It can, however, produce systematic errors. Trial and error is an important heuristic that may be used in a variety of situations, from cross-linking nuts and bolts to determining the values of given input variables in mathematical puzzles. Additional hypotheses, visual illustrations, simplification, and forward or backward reasoning are all common heuristics in mathematics.