Outline the Euthyphro's dilemma

In the Platonic dialogue Euthyphro, Socrates asks the greek prophet Euthyphro the question: "is the pious pious because it is loved by the gods or is it loved by the gods because it is pious?", that is: is the fact that the gods love a certain action or thing that makes that action or thing pious, or is it the case that there are actions or things that are pious and, because of that, are then loved by the gods? This question is known as the Euthyphro's dilemma. Over the years, the dilemma has become one of the most famous ethical dilemmas in the form: is what is morally good that is commanded by the gods or is what is morally good commanded by the gods because it is morally good? Let's divide the question in its two horns (a) and (b) and understand why it is a dilemma. (a) Is the morally good action the one that is commanded by the gods? If the answer to the question is that morally good actions are the ones that the god commands, then it seems that moral goodness is extremely arbitrary. In fact, the god could change his mind and stop commanding what he commands. If moral goodness equates to what the god commands, then as soon as the god changes his mind, what is morally good changes too. Furthermore, it is possible to imagine a world in which the god loves and commands actions that we consider bad actions, like the act of killing innocent people. Would the loving and commanding of god make the act of killing innocent people a morally good action? It seems plausible to say that the answer is no. Moral goodness seems to be more than just being commanded by the god. So the first horn of the dilemma is problematic. (b) is the morally good action commanded by the gods because it is morally good? Let's say that the god commands what is morally good because it is morally good. Then it seems like there is something that is moral goodness and that is not merely what the gods command. This solution to the dilemma seems to be a problem for a religion that conceives the god as being omnipotent. In fact, if the god does not have the power to decide what is morally good and what is morally wrong, then it seems like the god cannot be omnipotent. This horn of the dilemma is then problematic, if one believes in the fact that the god is omnipotent. This is the Euthyphro's dilemma.