# Set theory spring2022

1. (4) List exactly four elements of each of the following sets.

a. {π¦ | π¦ ππ π ππππ‘πππππ‘}

b. {5π | π ππ ππ πππ‘ππππ, π ππ πππ}

2. (6) List all elements of the following sets as a set. All answers must be exact and not

rounded.

5

a. {π | π β {10, 15, 20, 25, 30}}

b. {π β π‘βπ πππβππππ‘ | π πππππππ β²πβ²}

*note that precede means βcomes beforeβ

c. {π ππ ππ πππ‘ππππ | π ππ π ππππ‘ππ ππ 343}

3. (6) Describe the following sets using proper set-builder notation as explained in

your book. You may not simply list the numbers.

a. {0, 3, 8, 15, 24, 35}

b. The rational numbers that are strictly between -3.5 and 3.2

c. The negative odd integers that are multiples of 3

4. (8) Let A = {a, b, c, 1, 2, 3, q, r, s}, B = {a, 1, r}, and C = {a, 3, q, x, y, z}. Which of the

following statements are true? Which are false? Explain each answer in complete

sentences. Answers without explanation will receive no points.

a. 5 β π΄

b. π§ β π΄

c. π΅ β π΄

d. {1, 3} β π΄

e. {1, 3} β π΄

f. π΄ β π΄

g. π΅ β π΅

h. β
β πΆ

Number 4 continuation

5. (20) Let A, B, and C be as in #4 and let U = {1, 2, 3, 5, 7, 8, 9, a, b, c, q, r, s, f, g, x, y, z}.

Determine:

a. π΄ β© π΅

b. π΄ β© πΆ

c. π΄ βͺ π΅

d. π΄ βͺ πΆ

e. π΄ β π΅

f. π΄ β πΆ

g. π΅ β π΄

h. πΆ β π΄

i. π΄πΆ

j. π΄ β¨ πΆ

Number 5 continuation

6. (8) Given that U = all students at Valencia, I represents all IT students, P represents

all part-time students, and F represents all students on financial aid, draw Venn

diagrams (make sure to use circle shapes if you are typing the answers or use tools

to draw exact circle shapes if you are handwriting the answers) illustrating this

situation and shade in the following sets:

a. Non part-time IT students that are on financial aid

Need to show answer for this one with a separate Venn diagram.

b. Part-time IT students not on financial aid

Need to show answer for this one with a separate Venn diagram.

(I will assign zero points if you do not draw separate Venn diagrams for part a and

part b.)

7. (10) Given that U = all students at UCF, C represents all Chemistry majors, G

represents all graduate students, and F represents all full-time students. Let |U| =

60,000, |C| = 1200, |F| = 32,000 and |G| = 11,500. Also assume that the number of

graduate chemistry majors is 180, 130 of which are full time, and that there are 700

full-time chemistry majors. Determine the number of students who are:

a. Full-time non-graduate Chemistry majors

b. Graduate students majoring in something other than chemistry

c. Full-time students majoring in something other than Chemistry

8. (8) Let A = {1, 2, 3} and B = {c, d, f} and let U = {1, 2, 3, 5, a, b, c, d, e, f}. List the

elements of:

a. π΄ Γ π΅

b. π΄ Γ π΄πΆ

9. (5) List all 3-elements sets in the power set of {98, p, r, q}.

10. (5) Find the binary representation of 325 using the algorithm from section 1.4.

(Must show all work and must use this method only)

11. (5) Find the binary representation of 1,714 using the algorithm from section 1.4.

(Must show all work and must use this method)

12. (5) What positive integer has this binary representation (must show all the work):

1101111100011

13. (5) Calculate the following series (your final answer will be a number) showing all

work:

6

β(π 2 β 2π)

π=1

14. (5) Verify the following for n = 6 (by expanding both sides and showing they are the

same using algebra)

π

π

π

β(ππ + ππ ) = β ππ + β ππ

π=1

π=1

π=1

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