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CSC175 Practice Assignment 1 Type Name: Directions: Download this file and save as lastnamePracticeAssignment1. Type all solutions on this document. Use equation editor when necessary. Upload Word document to Blackboard by Saturday at noon. Please color, highlight, and/or bold your work to differentiate it from the original questions. Thank you. Directions for equation editor: Choose INSERT tab, Click Equation (far right), and explore all your options! 

1) Let the universal set be U={0,1,2 ,…,13 ,14 } , A= {x∈U|x=2n ,n∈Z },∧B= {x∈U|x=3n+5 , n∈Z }. a) List the elements of A. b) List the elements of B. c) List the elements of Ac. d) List the elements of A∩B. e) Write A∩B in set-builder notation. f) List the elements of A∪B g) List the elements of ( A∪B )c. h) List the elements of B−A. i) List the elements of A⨁ B. j) True or False: B⊆ A. Why? k) True or False: {8 ,12 }⊆ A. Why? l) True or False: ∅⊆ A. Why? m) True or False: {6 }∈ A . Why? n) Find ¿ A∨¿. Why? o) List the elements of H= {x∈ A∨x>8 }

2) At Living Academy, there are 170 seniors. In an activities survey, they were asked what activities they participated in during their high school experience. Here are the results: 72 in athletics, 81 in music, 43 in theatre, 27 in music and theatre, 18 in music and athletics, 6 in theatre and athletics, and 6 were in all three activities. Create a Venn Diagram (create your own or edit the attachment in Blackboard using Paint) and answer the following questions. a) How many seniors participated only in athletics? b) How many seniors participated in music but not theatre? c) How many seniors participated in athletics and music but not theatre? d) How many seniors participated in none of the activities?

3) Let C={r , o ,b } and W={s , t , n }. a) List C×W b) Find ¿C×W∨¿ c) Is (n ,o )∈W×C? Why or why not? d) Find the power set of W . (i.e. P( {s , t , n }))

4) Make the following conversions. Show work for credit. a) Convert the hexadecimal number 2BC4 to an integer. b) Convert the binary number 110110010 to an integer. c) Convert 1763 to hexadecimal. d) Use the algorithm (Ex 1.4.1) in the textbook to find the binary representation of 431. (Show each step of the algorithm)

5) Calculate each expression (show work) Hint: Review the examples in the PowerPoint before you attempt these

a) ∑ i=0

3

(2 i−1)

b) ∑ k=1

n

(k3+k) for n=2,3,4

c) ¿ i=−1¿3 {x∈Q∨i−1<x≤ i } d) ¿ i=−1¿3 {x∈Q∨i−1<x≤ i }

e) ∏ n=1

4

(−2 )n

6) Edit the attachment in Blackboard using Paint to shade each region given in set notation:

a) ( A−B )∪C b) Ac∩B c

7) Given the figure to the right, express the area in set notation.