Discreet Mathematics
posted by Chuck .
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.

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).