Question

What opposing beliefs do Antigone and Creon represent in Sophocles’s Antigone?

Answer 1

The opposing beliefs that Antigone and Creon represent in Sophocles’s Antigone is loyalty to family versus loyalty to the state.

Antigone buried Polynieces as she wanted that the family should do the burial rights after the death. Creon didn't want Polynices' body to go through the privilege of burial because he considered Polynices as a traitor. Creon is the king of Thebes who is arrogant and who never turns back. Also, he is obsessed with the civil laws and cannot bear anyone disobeying it. He is stubborn, full of pride and only believes in his words and decisions. This is very well known to the audience that it is Antigone who has buried Polynieces but the other characters are unknown of this.

Answer 2

I would say that the two of them represent these opposing beliefs: loyalty to family versus loyalty to the state. 
Because Antigone did everything for her family, whereas Creon cared more about the state he was ruling.