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1. (A) Explain what is meant by a stable matching and show, using your own example, how the Gale-Shapley deferred acceptance algorithm can generate a

1. (A) Explain what is meant by a stable matching and show, using your own example, how the Gale-Shapley deferred acceptance algorithm can generate a stable matching. [50 marks]

(B) Show, using your own example, that a stable matching may not exist in the so-called roommate problem. How would you match roommates in cases like this? [50 marks]

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