Nov 29th, 2013
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Chapter 7:
Which relations in Exercise 5 are partial orders?  Which are equivalence relations?                
For A = {a,b,c,d,e}, the Hasse diagram for the poset (A,ℛ) is shown in fig. 7.23.                
a.  Determine the relation matrix for ℛ.                      
b. Construct the directed graph G (on A) that is associated with ℛ.                
c. Topologically sort the poset (A, ℛ).                      
Let A = {1,2,3,4,5,6,7,8}.  In how many ways can we partition A as A1 U A2 U A3 with:                
a. 1,2 ∈ A1, 3,4 ∈ A2, and 5,6,7 ∈ A3?                      
b. 1,2 ∈ A1, 3,4 ∈ A2, 5,6 ∈ A3 and |A1| = 3?                      
c. 1,2 ∈ A1, 3,4 ∈ A2, and 5,6 ∈ A3?                      
Chapter 8:
In how many ways can Troy select nine marbles from a bag of twelve, identical except for color, where three are red, three blue, three white, and three green.

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