Math 102
Practice Test 1- Sets
Show your work wtrenwer appropriate for full credit
unless
indicated
otherwise)
{, '1t1n_r"_l!y
1. Give an exampleof a finite set that is not in roster notation that is well defined.
A= {x:x rE ^ Jo\. ,.r.1.. boFetno ^^}rIo?
2. Write out the set {x: x is an integer less than 4} in roster notation.
| "oi'-z''l'o
"'z'i\
3. Howmanysubsets
of {a"b, c, d, e, I h, i] arethere?showhowyoudetermined
it.
zY= Ls
ZSL sAsztS
Y,* {.d'*,\
4. Write each of the following in set builder notation.
tS orr. ,^L,.r kn+*..l -l o^I €l
a.{0,1,2,3,4,5,6,7} fX:X
b. {January,February,March,April,May}
{x; X rS 4,''-+h oFllt ,.*
teFeaaDecq"}I'
U'=d
5 . G i v e n U : { 1 ,2 , 3 , 4 , ' . 5 , 6 , 7 ,g9}, , A : { 2 , 1 , 6 , 9 } , B : { 1 ,3 , 4 , 5 , 7 }C : { 7 ,g } f i n d :
a.AnB ja?
e.(Atc)n(AuB)
b.B,= tz,e ft,cl\
= tgl
't = I e'l-- 8
1{7 Lt,r,3,r,t,Er,sl
6. List all the zubsetsof {t, i, m}.
^J,i
!A{i}, 1^?,{ti1,6
7- Cinthia has237 minutes remaining on her cell phone this month and wants to use thern
about equal to call her 1l good friends. Show how to use compatible numbers to
deterrnine the number of minutes she can talk to each of her friends.
7. Show that the set of whole numbers is infinite.
Zt{O _ o)roS Zrl *,^,fq9
0 1 2
lo
^
1
^
2
3
^
^
3 4 5
4
^
...n-1 7. ab"-f f,tl n,^,f.1
^
... n
r._r'*^A
*&
\ r'- I'
8. What doesthe shadedregion in each figure below representin set notation?
\
U
. ,l
Y
dr
Snt)-a
Tf-
9. Illustrate eachof the followingby shading the Venn diagramsbelow.
a. S'fl K
10. Use the diagrzimbelow to find the cardinality for eachproblem.
U
76
a r?(N):
b.n[(R0E) U N] : lO
\6 +t+q*ut
6\
d. n(E- R)
5Ll
Lll+t\
4 f 7+r { +
t\+ 1- l
e.n(u) 2rj
1 6 +26+r{}a+\ +t\\ +\l +l-7
c.n(E'): l'-15
tb126 +L{r3-1
f.ru(RnEnN)l
fi^
\ry
'rt'
,/ 1D
H
the statementto make
1 1. Tell whether eachstatementis true or false, if false correct
it true'
a. All sets that are equal are also equivalen!'
f r,r,5i;{p;,9):, ;-..,:;."';.;l
,!.tob$
b. A'
Gr:
5 of this test)
i tl
A'nD't
,1,8\
rrffi-t\,?,5,s,6
the number of subsetsfor
l(nt
''
{Jsn
12. Use the Venn diagram below to fill in the missing statement(l pt/problem).
' y1l=301
t'= 3V
M
16
Ft
a.n(M'uC'): 5F
b.n(-l----):36
-Yinol
ctn(wtr
13. Use the Venn diagram to work the fol lowing problem in three stepsA' t ,(B nC)p
€n e-
t
I
A,/
I@''-Va
14.Fill in theblankswith oneof the following €, E, e, g', c., or q_ to makeeaeh
statementtrue(lpt/problem).
(Ar\t1 "1
lf
,)
lLr,
{ O,t)
a. { } & {2, q}
b. Whole 4 Rationalnumbers
d.{-c
A\
c_
c. --2 $-Naturals
numbers
d. -6 e
{x:x is a solutionto the equation* :36}
15. Therewere 100studentsin the library who respondedto how they completedtheir
researchpaper.
-*&studentsonly usedthe periodicalsP
-2ffits
usedthe web andbooks hrffi
Z"\-t( : l1
J5-studentsusedbooks,the web,andperiodicals
raffirdrnts usedbooksandperiodicals
2o rrsedtheweb andperiodicals
'Skdentsusedbooks+ldo--7 - C'79
-*SSdentsdid not usethe web,nor books,nor the periodicals.
a. Represent
this informationwith a Venndiagram.
PPe""dtty
W-- 'eeb
ls {E
A tbr,Vs
-l-tB
N = 1 0 0 - --7L - L f - l t - f i
A1*tf = t(
b. How many studentsusedthe web in their research?
c. How many studentsusedbooks orperiodicals?
b
Llq
c. g1
16' concenringthe first 41 presidents
of the united Stateswe know thefollowing
facts:
ate,e,
pgsitio,gs(Spt).
'\I
How manypresidents
servedin:
a. noneof these3 positio"s?_15__
b . only in the U.S. Senate?__14__
c. at_lggtoneof the threeposition?€la__
d. exactlytwcipositions?*!__
17' List thenumberedregions
thatmakeup the answerto eachof
the following:
U
t
a.A-C:
TT
J:
tl'.
\
.l
1
b.B,n.A: T- ., JU_
7-
c. ,4.u(B n C)-tr
,fja ,rz, vt,rzTT
d. C n (B uA), Wr_TT
%
18. Use DeMorgan's Laws and set operationsto
write the shadedregion in nvo different ways.
=-T' n n'
(.oun)'
19. Apizza chain is willing to pay $0.75 to eachperson interviewed abouthis or her likes
and dislikes of types of pizza crust. Of the people interviewed, 22Aliked thin crust,
270 liked thick crust, 70 liked both, and 50 did not like pizza at all. What was the
total cost of this survey? (3 pts).
47o.,Y.1,
20.|nasrrrveyofl30people,thefollowingdatawereco1lected:@d
29 peepl.e subscribed to magazines, and-17 people-werernembers
of amailCD club. Md+obo
eeopte S*scrn"A*n
ma
ines"f
er4s"ose€D€lub, and *$people
s
sulrscribedloboth the newspaper andmagaAnes and were members of a mail CD
club. Make and fill in a Venn diagram to illustrate this situation (3pts).
Bonus Problem: (3pts) Describe
Explain the Three-Way Principle.
a one-to-one correspondence between
the set {1/8, 1/27, 1/64, 1/125, ...}
Soi.,ec,.prrbh'^and
v!l) one
3 9kr\<37c9,
of its proper subsets.
V 1 6 .r^\l p t" h;,. V
!rn 1 -l r|t,
1/8
1/27wil\
1/64nu*!*J
1/125 ... 1/(n+1)^3
1/27 1/64 1/125 1/216 ... 1/(n+2)^3
t)
46