What properties does the sameShirtColor relation have?

"Let sameShirtColor be an endorelation on the set of all crew members of the Enterprise, where (x, y) ∈ sameShirtColor if character x ordinarily wears the same shirt color as character y. Is sameShirtColor reflexive? Yes, since you can’t help but wear the same shirt color as you’re wearing. Is sameShirtColor symmetric? Yes, since if a crew member wears the same shirt color as another, then that second crew member also wears the same shirt color as the first. If Scotty and Uhura both wear red, then Uhura and Scotty both wear red, duh. Is sameShirtColor antisymmetric? No, for probably obvious reasons. Is sameShirtColor transitive? Yes. If Kirk and Sulu wear the same color (yellow), and Sulu and Chekov wear the same color (yellow), then Kirk and Chekov most certainly will wear the same color (yellow)."