Problem 2 Audrey, Donna, Shelly, and Laura are four students who must form pairs

Question

Problem 2 Audrey, Donna, Shelly, and Laura are four students who must form pairs to do a school project. The preferences are as follows rew nna Shelly aura DonnaShlly Laura Donna Shelly Audrey Donna Shelly Laura Laura Audrey Audrey ote that the problem is a bit different from the mathching prob- lems we have seen before. Specifically, the players are not divided into two groups. Dividing them into two groups and running an algorithm does not guarantee a stable matching. a) Is it possible to match the girls into pairs such that no two girls who are in different pairs would like to leave their current partners and form a pair? Give an example or show that it is impossible b) Now, su that the preferences are: helly Laura onna udrey D Donna Shelly Audrey Audrey na onna aura aura ura S it possible to match the giris into pairs such that no two girls who are in different pairs would like to leave their current partners and form a pair? Give an example or show that it is impossible

Explanation / Answer

Ans a It is not possible to form two pairs because in the table each girl have the all other three and there is not possible to leave current partner and form a pair.

b. It is not possible that two girls in different pairs would like to leave their current parters because it it happen it leads to duplicacy and from the above data it is not possible to form a pair.

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