# Week 3 Answers Essay

627 Words Jan 24th, 2014 3 Pages
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,
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?

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