Posted by Chuck on .
Part I: 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}
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 (or were) a member of which team(s). (Show the relation in the following forms:
◦Set of ordered pairs
◦Directional graph
2.Is the relation a function? Explain.
3.Now, use set Q as the domain, and set D as the range. Show the relation in the following forms:
◦Set of ordered pairs
◦Directional graph
4.Is the relation a function? Explain.

Discreet Mathematics 
Anonymous,
For the first problem the ordered pairs are (Jets, Namath) (Giants, Manning) (Cowboys, Aikman) (49ers, Montana) (Chiefs, Montana) (Patriots, Brady). The directional map is scanned and attached. This is a function. No one element of the domain matches more than one element in the range.
For the second problem, reverse the ordered pairs and find that it is no longer a function, since one element of the domain (Joe Montana) matches with two elements of the range (49ers and Chiefs).