We would usually only diagram conditional statements, but I can explain the logic behind (E). The argument tells us that Damon can only get the paper done in time if he works without interruption. But his daughter has a dance recital and he promised to take her there and go to ice cream afterwards. It means that he cannot fulfill both his professional and family responsibilities - two situations cannot occur at once because something necessary for one situation (he must take the daughter to her recital) is incompatible for another situation (he must work uninterrupted). Therefore, since these necessary conditions are mutually exclusive, the argument proceeds by saying that he could only pick one - take the daughter (family) or finish the paper (professional responsibilities).