Chapter 5, Problem 24E

The Kangaroo Lodge of Madison Country has $10$ members ( $A,B,C,D,E,F,G,H,I$ and $J$). The club has five working committees: the Rules Committee ( $A,C,D,E,I,$ and $J$), the Public Relations Committee ( $B,C,D,H,I$ and $J$), the guest speaker committee ( $A,D,E,F,$ and $H$), the New Year’s Eve Party Committee ( $D,F,G,H,$ and $I$), and the Fund raising Committee ( $B,D,F,H.$ and $J$).

a. Suppose we are interested in knowing which pairs of members are on the same committee. Draw a graph that models this problem. (Hint: Let the vertices of the graph represent the members.)

b. Suppose we are interested in knowing which committees have members in common. Draw a graph that models this problem. (Hint: Let the vertices of the graph represent the committees.)