# MTH/221 DISCRETE MATH FOR INFORMATION TECHNOLOGY

**Question description**

Chapter 7: | ||||||||||||||

7.1-6 | ||||||||||||||

Which relations in Exercise 5 are partial orders? Which are equivalence relations? | ||||||||||||||

7.3-6 | ||||||||||||||

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). | |||||||||||||

7.4-2 | ||||||||||||||

Let A =
{1,2,3,4,5,6,7,8}. In how many ways
can we partition A as A_{1} U A_{2} U A_{3} with: |
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a. | 1,2 ∈ A_{1}, 3,4 ∈ A_{2}, and 5,6,7 ∈ A_{3}? |
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b. | 1,2 ∈ A_{1}, 3,4 ∈ A_{2}, 5,6 ∈ A_{3} and |A_{1}| = 3? |
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c. | 1,2 ∈ A_{1}, 3,4 ∈ A_{2}, and 5,6 ∈ A_{3}? |
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Chapter 8: | ||||||||||||||

8.1-12 | ||||||||||||||

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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