5. [10 pts] The MCIT TAs are huge fans of the Marvel universe, so they decide to perform a thought experiment on the Marvel universe. They notice that the Marvel universe has 21:: superheroes that are related to each other by ghts they have fought together, such that the universe has It relationships between superheroes that have fought together, where k is a positive integer. Prove that if each superhero in the Marvel universe has fought with at least one other superhero, then the Marvel universe can be partitioned into exactly I: groups of superheros such that in each of these groups any two superheros are connected to each other through a path of fought-together-relationships, and, moreover, each of these groups is maximal with this preperty