1. Express the following in roster form: Set M is the set of natural numbers between seventeen
and twenty-three.
{18, 19, 20, 21, 22}
2. Can the word "RATES" be played from the letters A, E, O, N, R, S, T as the first move
in a Scrabble game? Explain your answer.
Yes, because {R, A, T, E, S} is a subset of {A, E, O, N, R, S, T}.
3. Are the two sets equal, equivalent, neither or both? Explain your answer.
V = {coal, wood, gas, electric, solar}; W = {football, baseball, soccer, hockey, rugby}
The two sets are equivalent because they both have the same number of elements.
The two sets are NOT equal, though, because they do not have the same elements.
4. Given U = {10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}, A = {12, 14, 16, 18, 20}, and B = {11,
13, 14, 15, 18, 19, 20}.
Find A′ ∩ B′. Do not skip to the answer. Show your work, finding A’, then B’ then find their
intersection.
A’= {10, 11, 13, 15, 17, 19}
B’ = {10, 12, 16, 17}
A′ ∩ B′ = {10, 17}
5. Given the following sets, select the statement below that is NOT true.
A = {l, a, t, e, r}, B = {l, a, t, e}, C = {t, a, l, e}, D = {e, a, t}, E = {t, e, a}
(Points : 2)
C⊂D
E⊆A
D⊆C
C⊆B
D⊂A
6. Using correct mathematical notation and symbols, express the following in set-builder
notation: Z = {4, 5, 6, 7, 8, 9, 10, 11}.
Z = { x | x " #, 4 $ x $ 11}
7. A car dealership interviewed every driver who came onto their lot on Tuesday. This produced
! the following results: there were 61 people who owned trucks and 115 people who owned cars. If
14 people owned both a truck and a car and 8 people owned neither, how many people were
interviewed?
61 + 115 – 14 + 8 = 170
8. An electronics store surveyed every 12th customer who came into the store for a week.
Of the 370 people who responded,
159 people watched movies on VHS tapes.
263 people watched movies on DVDs.
64 people watched movies both on VHS tapes and DVDs.
Create a Venn diagram to reflect the above data, label your diagram clearly. Use your diagram to
answer the following questions here.
i. Of those surveyed, how many watched only VHS tapes? 95
ii. Of those surveyed, how many watched only DVDs?
199
iii. Of those surveyed, how many watched VHS tapes or DVDs, but not both? 95 + 199 = 294
iv. Of those surveyed, how many watched VHS tapes or DVDs, or both? 95 + 64 + 199 = 358
9. A survey of flower gardeners showed the following:
87 grew roses
15 grew both roses and tulips
8 grew all three types
27 grew tulips
11 grew both orchids and tulips
7 grew none of these three
26 grew orchids
19 grew both roses and orchids
Create a Venn diagram to reflect the above data, label your diagram clearly and submit to the
Dropbox. Use your diagram to answer the following questions here.
(a) How many grew only orchids? 4
(b) How many grew both roses and orchids, but not tulips? 11
(c) How many grew only roses? 61
(d) How many grew none of these three or only tulips? 7 + 9 = 16
(e) How many flower gardeners were surveyed? 110
10. Given A = {1,2,3,4,5,6}, B = {1,2}, and C = {6,7}. Evaluate each set
a) A ∩ B = {1,2,3,4,5,6} ∩ {1,2} = {1,2}
b) A U C = {1,2,3,4,5,6} U {6,7} = {1,2,3,4,5,6,7}
c) B U C = {1,2} U {6,7} = {1,2,6,7}
d) (A U B) ∩ C = ({1,2,3,4,5,6} U {1,2}) ∩ {6,7} = {1,2,3,4,5,6} ∩ {6,7} = {6}
e) A U (B U C) = {1,2,3,4,5,6} U ({1,2} U {6,7}) ={1,2,3,4,5,6} U {1,2,6,7} = {1,2,3,4,5,6,7}
f) (A ∩ B) ∩ C = ({1,2,3,4,5,6} ∩ {1,2}) ∩ {6,7} = {1, 2} ∩ {6, 7} = { }
g) (A ∩ B) U C = ({1,2,3,4,5,6} ∩ {1,2}) U {6,7}= {1, 2} U {6, 7} = {1,2,6,7}
(Points : 7)
11. Given the diagram below, find P U Q. Write in correct set notation.
Two circles overlapping each other
In the left green circle right outside is P. right inside is P and E
In the middle of the green and the red is S,N,A.
In the red circle is C and K.
Right outside the red circle is Q. Please try and draw this out and answer the question.
The way I interpret this is that the green circle is set P, and P = {P, E, S, N, A}; and the red circle
is set Q, and Q = {S, N, A, C, K}
The union of the two sets is:
P U Q = {P, E, S, N, A} U {S, N, A, C, K} = {P, E, S, N, A, C, K}