Basic challenge (or challenges) to justice Thrasymachus, Glaucon, and Adeimantus

  What is the basic challenge (or challenges) to justice Thrasymachus, Glaucon, and Adeimantus put forth in Republic? What do they argue about justice and injustice? In what way does Socrates, using the account of justice in the city and in the soul he develops in the republic, answer this challenge? How does he try to show that justice is worthwhile or valuable? Do you think his answer succeeds? If so, why? If not, why not?