Problem 7. Relations (11 points) Let T be a set of soccer teams: T= IClub America, Philadelphia, Chelsea, Arsenal, Orlando, Pachuca We say that team x is "affiliated" with y if they played or will play against each other in the 2022-23 season or pre-season. Let us define the relation "affiliated" (xAy) as a subset of the cartesian product TT. That is: xAy=1 (Club America, Chelsea). (Club America, Pachuca), (Philadelphia, Orlando), (Chelsea, Club America), (Chelsea, Arsenal), (Arsenal, Chelsea), (Arsenal, Orlando), (Orlando, Arsenal), (Orlando, Philadelphia), (Pachuca, Club America), (a) [ 3 pts.] Is the "affiliated" relation symmetric? Why or why not? (b) [3 pts.] Is the "affiliated" relation transitive? Why or why not? (c) [3 pts.] Is the "affiliated" relation reflexive? Why or why not? (d) [2 pts.] Is the "affiliated" relation an equivalence relation? Why or why not