Complete 10 questions below. Please review the rubric posted in week 1 for math problems. Submit to your assignment tab. Submit a certificate of originality for this assignment. Exercise 7.1 – Problem 10a
If A = {w, x, y, z}, determine the number of relations on A that are (a) reflexive; Total reflexive pairs is 2n^2-2
N2-2 = 12. Therefore, 212 Relations Exercise 7.1 – Problem 10b
If A = {w, x, y, z}, determine the number of relations on A that are (b) symmetric; Total reflexive pairs is 2(n^2+n)/2
(n2+n)/2 = 10. Therefore, 210 Relations Exercise 7.2 – Problem 15a
Draw the digraph G1 = (V1, E1) where V1 = {a, b, c, d, e, f } and
E1 = {(a, b), (a, d), (b, c), (b, e), (d, b), (d, e), (e, c), (e, f ), (f, d)}. Hand drawn diagraph submitted with assignment. Exercise 7.3 – Problem 1
Draw the Hasse diagram for the poset (P(U), ⊆), where U ={1, 2, 3, 4}. Hand drawn diagram submitted with assignment. Exercise 7.3 – Problem 6a
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.

The matrix is as follows:
11111
01011
00111
00011
00001

Exercise 7.4 – Problem 1a
Determine whether each of the following collections of sets is a partition for the given set A. If the collection is not a partition, explain why it fails to be. a) A = {1, 2, 3, 4, 5, 6, 7, 8}; A1 = {4, 5, 6}, A2 = {1, 8}, A3 ={2, 3, 7}

The collection IS a partition as it meets all 3 rules for partitions. Exercise 7.4 – Problem 2a
Let A _ {1, 2, 3, 4, 5, 6, 7, 8}. In how many ways can we partition A as A1 ∪ A2 ∪ A3 with a) 1, 2 ∈ A1, 3, 4 ∈ A2, and 5, 6, 7 ∈ A3? There are 3 ways we can partition A. Exercise 8.1 – Problem 4
Annually, the 65 members of the maintenance staff sponsor a “Christmas in July” picnic for the 400 summer employees at their company. For these 65 people, 21 bring hot dogs, 35 bring fried chicken, 28 bring salads, 32 bring desserts, 13 bring hot dogs and fried chicken, 10 bring hot dogs and salads, 9 bring hot dogs and desserts, 12 bring fried chicken and salads, 17 bring fried chicken and desserts, 14 bring salads and desserts, 4 bring hot dogs, fried chicken, and salads, 6 bring hot dogs, fried chicken, and desserts, 5 bring hot dogs, salads, and desserts, 7 bring fried chicken, salads, and desserts, and 2 bring all four food items. Those (of the 65) who do not bring any of these four food items are responsible for setting up and cleaning up for the picnic. How many of the 65 maintenance staff will:

(a) help to set up and clean up for the picnic?
4 people bring nothing, so therefore 4 people will setup and clean up the picnic
(b) bring only hot dogs?
2 people only bring hot dogs
(c) bring exactly one food item?
24 people bring exactly one food item

Exercise 8.1 – Problem 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?

220
I am not sure about this one. In fact I think I am wrong….not sure how to build in the color into my calculations…. Exercise 8.2 – Problem 4
Let A = {1, 2, 3, . . . , 10}, and B = {1, 2, 3, . . . , 7}.
How many functions f : A→B satisfy |f (A)| = 4?
3440640

How many have |f (A)| ≤ 4?
3910669