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.)
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.)
Solution Summary: The author illustrates how to model a situation in which we can find out the pairs of members in the same committee
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.)
For what value of A and B the function f(x) will be continuous everywhere for the given definition?..
Please fill in the rest of the steps of the proof of Thm 2.5. Show how "Repeating this step with n-1,n-2,...,2 in place of n" gives us the desired result.
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