Plato on the nature of morality/justice and its value

Plato on the nature of morality/justice and its value   Order Description   What is Thrasymachus' challenge? What is Glaucon's challenge? How do they differ? (Though there is some overlap, so don't focus on the aspects of Thrasymachus' challenge that are simply repeated by Glaucon). How does Socrates meet these challenges, in his conversation with Thrasymachus, and in the Republic as a whole. Are the responses successful? Why or why not? Instead of treating the essay like a list of short answer questions, my professor would like it to be a brief, integrated essay on the topic, but also touching base on all of the issues those sub-questions raise. He has two pet peeves that he does not want to see in the essay. He does not want the word "Relatable" included, nor does he want the sentence "that begs the question". We have only been reading Republic, by Plato, so I assume that is the only source allowed for the essay.