Question
The original Stable Marriage Problem is stated as follows: Given n men and n women, where each person has ranked all members of the opposite
The original Stable Marriage Problem is stated as follows: Given n men and n women, where each person has ranked all members of the opposite sex with a unique number between 1 and n in order of preference, marry the men and women off such that there are no two people of opposite sex who would both rather have each other than their current partners. If there are no such people, all the marriages are "stable". Let us consider a modified version of this problem: Given n men and n women, where each person has a set of preferred people of opposite sex that they say they could marry to. Find a marriage arrangement for all people so that each person is married to one of those that he/she prefers. Some examples for n=3 are given below. Let us denote the men by mi and the women by wi, respectively. If the preference of m1 is {w2,w3}; m2 is {w2,w3}; m3 is {w1}; w1 is {m3}; w2 is {m1,m2}; and w3 is {m1,m2} then the arrangement (m1,w2), (m2,w3), (m3,w1) is a solution to the problem. On the other hand, if the preference of m1 is {w1}; m2 is {w2,w3}; m3 is {w1}; w1 is {m3}; w2 is {m1,m2}; and w3 is {m1,m2} then the problem has no solution. Represent the problem as a knowledge base whose models represent the solutions of the problem. Make sure that your solution is correct by checking your representation with the two examples. Provide arguments for the correctness of your solutio
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