Task Background: Suppose you are developing a statistical database in which information about professional football teams and records are stored.
Consider the following 2 sets of data that list football teams and quarterbacks:
D = {Jets, Giants, Cowboys, 49’ers, Patriots, Rams, Chiefs}
Q = {Tom Brady, Joe Namath, Troy Aikman, Joe Montana, Eli Manning}
NOTE: (You can also use http://www.pro-football-reference.com to find this information, but here it is as well :)
The following list gives you the relationships (mapping) between team and QB. * Jets – Joe Namath * Giants – Eli Manning * Cowboys – Troy Aikman * 49’ers – Joe Montana * Patriots – Tom Brady * Rams – Joe Namath * Chiefs – Joe Montana

1. Using D as the domain and Q as the range, show the relation between the 2 sets, with the correspondences based on which players are on which team. Show the relation in the following forms:
Set of ordered pairs (20 points)
Directional graph (like the pictures draw in class in our live chats – see HINT below). (20 points)
The ordered pairs when D is the domain are:
{(Jets,Joe Namath),(Giants,Eli Manning),(Cowboys, Troy Aikman),(49ers,Joe Montana),(Patriots,Tom Brady),(Rams,Joe Namath),(Chiefs, Joe Montana)}

2. Is the relation a function? Explain. (10 points)
This is a function, because every element (Quarterback) of the domain is mapped to exactly one unique element (Team) of the range. So with the one to one relation of player to team, that makes this a function. 3. Now, use set Q as the domain, and set D as the range (reverse). Show the relation in the following forms:
Set of ordered pairs (20 points)
Directional graph (20 points)
The ordered pairs when Q is the domain are:
{(Joe Namath, Jets),(Eli Manning, Giants),( Troy Aikman, Cowboys),( Joe Montana,49ers,),(Tom Brady, Patriots),(Joe Namath, Rams),(Joe