Hobbes gives a familiar kind of justification of the state: he shows why people who didn’t have one would want to create it. That is the same broad method that Glaucon and Socrates used (though Glaucon thought that his account undermined the case for justice).
In Hobbes’s case, the justification for the state comes from considering what is called the state of nature: what life would be like without a state. I presented his ideas about the function of the state in contrast with Plato’s and Aristotle’s. Then we talked about some specific questions about how the arguments in chapters 11 and 13 worked.