Spring 2011
Nlath 110
PracticeTest 2
1.
Tel1 whether the conditional is true or false. Here T represents a true statement and F represents
faise statement.
(1>5)-+F
Is the conditional true or false?
i-'i
il.,
2.
false
true
Let s represent 'she has a pet turtle, '1et t represent 'he trains tigers,' and let r represent 'they raise
monkeys.'Express each compound statement in words'
What are the words that express the conditional statement?
;l',.i If she has a pet turtle, then they do not raise monkeys and he trains tigers.
i,::,' If she does not have a pet turtle, then they do not raise monkeys and he ffains tigers.
;:" If they do not raise monlceys, then she has a pet turtie or he trains tigers.
i-:" If she has a pet turtle, then they raise monkeys or he trains tigers.
3.
Wnte the following statement in symbolic form'
"You]l enjoy yourphysics class if you understand the mathematics,
and
:
"You'l1 enjoy your physics ciass"
n = 'ryou understand the mathematics"
1: "you'llbe abie to do the homework"
Let p
What is the statement in symbolic form?
(q
-+ p) n r
':i
i*.r (q -+ p) v r
i": $-+q)vt
,1.: (p -+ q) n r
4.
Let b represent'I nde m}, bike,' let s represent'it snou,s,, and let p replesent
'tire piaf is postponed.'write tire compound statement in symbols.
If it
does not sno'il', then I ride my bike.
The statement is writlen symbolically as
-I - !'
a
5.
Let p represent a lme statement, let q represent
a false statement, and let r represent a true
statement. Find the tmth value of the given
statement.
Is the statement true or false?
t';
i:.,
6.
false
ffue
true statement' let q represent
a false slatement, and iet r represent a faise
given
statement' Find the truth value of the
Let p represent
a
statement'
-r-+(P"-q)
ls the statement true or false?
i.l
i-^i
7
true
false
p is false, q rs false' and r is true'
Determine the truth value for the statement when
-[('-+ -q) -+ (q'-r)]
The statement is
8.
Constmct
a
a--
I f.l.
truth table to verify the following equivaience'
First, compiete the truth table below'
p
q
p^q
T
T
T
T
F
F
F
T
F
F
F
F
qv(pnq) p--+q rn(p-+q)
T
L]
n
rl
is qv(pncf equivalent to qn(P-+q)
{-:
,- 1
F
L]
T
l--l
T
n
?
No
Yes
Ifshehasasnakeforapetandhetrainsponies,thentheyraisemonkeYs.
Pick the compound statement in symbols'
i*.:'
(snm) -+p
,:1,;" (mns)-+p
i:.r"
(mnp)-+s
'FerF.;'ffi#4F.':
'J'
(slrg)
-i'I'r'\
10.
Changethell,lhenstatementtotneequlvatenl(J-KSIaIe[IgrrL'
then I don't want to be right'
If loving you is wrong,
Piclc the equivalent statement.
{"i"
r-.:'
Loving you is wrong or I want to be right'
'i*;:'
Loving you is not wrong and I want to be right'
i:-
Loving you is not wrong or I don't want to be right'
Loving you is wrong and I don't want to be right'
l'
-;;;;;;;;;;,
,
,r"",r""
;
If
"",
contraposirive of the sraremenr below.
the birds flock together, then tirere must not be an early
worn'
The converse of the given statement is which of the following?
,:.t, If the birds do not flock together, then there must be an early wofin'
:'f
:.
L.:"
wofin'
The birds do not flock together or there must not be an eariy
If
there must not be an eariy wolTn, then the birds flock together'
If
there must be an early worm, then the birds do not flock together'
The rnverse of the given statement is which of the following?
,.1-:" The birds
do not flock together or there must not be an eari5'worn.
i.:;L,'
If
wonn'
the birds do not flock together, then there must be an eariy
If
there must be an early wonn, then the birds do not flock together'
fi'
If
tirere must not be an early wonn, then the birds flock together'
The contrapositive of the given statenent is which of the foliowing?
,1.:"
The birds do not flock togetirer or there must not be an earll' wolln'
,1.,= If
there must be an early wonn, then the birds do not floclc together'
,:r. if the birds do not flock together. then there must be an ear11'worrn.
i."' If there must not be an earil' wofin, then the birds flock together'
12.
Find the inverse and the contrapositive of the statement
n->-m
What is the inverse?
l__J
-|
What is the contraPositive?
Lr
T
L_1
the inverse, and the contrapositive'
For the following staternent, write the converse,
Use De Morgan's laws to simplify each'
t* !-qv-p).
What is the converse of r
ii
il.r
i";
{:
-+ (* q t' -
(qvp)+r
-r-+ (qvp)
-r-> (q"P)
(*qv-p)-+r
What is the inverse of r -+
i:
P)?
-r-+
(-
q'-
p)?
(q^p)
(- qt -p) -+ r
':
i.r -r-+ (q"P)
{i (qnP)-)"'r
What is the conffaPositive
ofr-+ (-q"-P)?
(qvp) -+ r
(q"p)-)-r
-r-+ (qvP)
|
14.
..'
^-r-+ (qnp)
Write the statement in the form'if p, then q'
All whole
numbers are rational'
Choosethestatementthatbestrewritesthesentenceinthespecifiedform.
If a number is whole, then it is never rational'
i.i.
ij"
"i;"
15.
If a number is rational, then it is never whoie'
If
a number is
whole, then it is aiways rational'
Identify the statement as ffre or false'
g
- g:0if
andoniYif
9:J + 2
ls the statement true or false?
i-;
*
true
faise
lo
the IOllowmg Statgment,
_FOt
.Wflte Ine OOnVCISg" Ll-tc lllvtrr.Li ouu lrrw lvrrlrq|vDrLr
which are equivalent.
"If you donlt pa1' your bills on time,
then your credit scole goes
dowl."
What is the converse of the statement?
i:.i^ If your credit score goes down, then you don't pav your bills on time.
then you do pay your bilis on time.
i].:"
If your credit score does not go down,
r:,"
If you do pay your bills on time, then your credit
score does not go down.
What is the inverse of the statement?
{.:" If your credit score goes down, then you don't pay your bills on time.
;.1_:" If you do pay your bills on time, then your credit score does not go down.
If your credit score does not go down,
l"
then you do pay your bills on time.
What is the contrapositive of the following statement?
i.,.i^ If your credit score goes down, then you don't pay your bilis on time'
i,l-i'
i:)'
If your credit
score does not go down, then you do pay your bilis on time.
If you do pay your bills
on time, then your credit score does not go down'
Which statements are equivalent?
,l-,,' If your credit score goes doum, then you don't pay your bills on time,
If you
i-.:'
do pay your
If your credit
If your credit
bilis on time, then your credit score does not go down.
score goes down, then you don't pay your bilis on time.
score does not go down, then you do pay your bilis on time.
,.,.:," If you do pay your bi1ls on time, then your credit score does not go down
If your credit score does not go dou'n, then you do pay your bilis on time.
i-,,
1'l
If you don't pay your bills on time, then your credit score goes down. ,
If you do pay your bilis on time, then your credit score does not go dowu.
Drau, a ctrcuit representing the foliou'ing statement'
(Pn
-s)n-q
What is a circuit representing the statement?
JF
d""-p
*:./*c1
hm*tr
q
w
.,r"
.# *'.
* -P
ffi',F
'Wr'-.\
w-
@
l*-q*
"r
w/
*'{; *''4' **'{ *'
r-,'
'
*"{" **'{s
*{q*
18.
circuit'
Find the logic statement representing the
Find the best solution.
il:" p^(-qw)
i*i- (pv-q)nr
i;" pv(-q'rr)
i-i" pn(qnr)
1q
Find the iogic statement representing the circuit'
Find the b'est solution.
ij^
i:i'
rj"
i.i"
pvqv-?
pvq^-P
p^q^*p
p^qv-P
2{)
Find the logic statement representing the circuit.
l-4
I
1,1
Find the best soiution.
'1,.;'^ pvlqn(qv-p) ]
i:" qnfpv(qn-p) ]
il,:" qvfpn(qv-p)]
il-;'' qvfqn(qv-p)]
21.
Consider the following statement'
If you attend movie night
and watch The Ring, you feel scared'
a. Use symbols to write this statement.
a. write the statement using symbols. Choose the correct answer belou''
r -+ (-p n -q)
(pnq)+r
(r+-p)v-q
Svq)+r
b.
Write the contrapositive of the statement. Choose the correct answer belou''
,
,
.
,
aa
If you drd not attend movie night and did not watch
night'
If you
movie
do not feel scared or did not watch The Ring, tiren you did not attend
If you
The Rlng'
do not feel scared, then you did not attend movte night or did not watch
If you
watch The Ring'
do not feel scared, then you did not attend movie night and did not
Identify the statement as true or false.
3-tI+6ilandonlfifS*8
Is the statement true or false.
i.-,;
:''
The Ring, then you don't feel scared'
True
False
23.
Identity the statement as tme or talse'
+
6 x 2: l4 if and oniY if 9 7 + 16
Is the statement troe or false'
ii
i;
74.
True
Faise
Identify the statement as true or false'
ThemoonismadeofgreencheeseifandoniyifHawaiirsastateoftheUnitedStat.es.
ls the statement ffue or false'
25.
i-'1
True
ii
False
Tell whether the statement is true or false'
Is the statement true or false?
i:r
il:'
26.
True
False
true or faise'
Decide whether the given statement is
r
e {2,3,9,
8}
Choose the correct answer below'
l:i
f-:i
27.
True
False
pairs are equal'
Given the foliowing sets, determine which
A= tu, e, j,k)
........
:........-......-...,-.-
a)A:C
i:i Faise
'*
True
b)c:D
i,; False
|r True
c)A=B
ir
True
I
False
C:
li,
k,e,a)
B- {*'Y-1"1*} D= {8,3:6:9}
2g.
Tell whether the statement is tme or false'
OeA
Is the statement true or false?
,:1": True
{,i
29.
Faise
Determine which of the following statements are true'
c) 6
a) {6}
{6}
c
d)It+j={t+}
c {6,14,17}
b)0E?
c {6, 14,17} true or false?
l.: False
Is {6}
Is0cAtrueorfalse?
tl:
Is 6
False
c
i::
{6} true or false?
False
c {14} true orfalse?
i*r False
is {1a}
30.
True
i*'.''
True
rt'*'t
True
il.r
True
Find the number of subsets for the foliowing set.
Hou'many subsets does this
il
31.
--'
Gto"
LetB:
*,=
a
whoie
set have?
number.)
:
{70,12,74,76} and C= {9,10,11,12,13}.
a:_
{ 10112}
Which symbol inserted in the bianh will make the above statement correct?
i:^ n
32.
i:i' €
LetD: {10,13,15},8:
{10,12,13,14}
List the elements in the set D
Du
E
= {LJ}
i.--:'
u
andF:
i-:"
e
[9,11,12,13'15]'
u E'
(Use commas to separate answers.)
whether the
Use the Venn diagram to determine
B'
statements are equal for al1 sets A and
41.
A'r, B and (A n B')'
Are A'
u B and (A n' B')' equal
statements?
Yes
No
A coilege suwey was taken to determine
,toa.ntlstudy. bf 101 students surveyed'
AQ
t()
where
64
in the
studied in the cafeterta, 56 studied
the cafeteria
student lounge, 24 studied in both
and the student lounge'
1y in the cafetena?
[
only in the student lounge?
Of those interviewed how many studied
[
lounge?
ofthoseinterviewedhowmanydidnotstudyineitherthecafeteriaorthestudent
49.
;t ;;;r.t*.r"o
to determine sPorts
16 had
teams. 22had soccer' 20 had rugby'
11 had
basketball, 13 had soccer and rugby'
and
soccer and basketball, 11 had rugby
basketbali. 7 had al1 three'
Let A = soccer, B
'c
\tIil
: rugbY, C : basketball'
How many had oniY a soccer team?
,:
not basketball?
How many had soccer and rugby, but
,I
Hou, many had soccer or rugbY?
T
basiretball?
How many had soccer or rugby, but not
,!
How many had exactilr two teams?
T
50
A single fair die rs tossed' Find
the probability of
roliing
a
number greater than
a number greatff than 1? [
What is the probabiirty of rolling
(Simplify your answff Type a fraction')
1
[
33.
:'t\1, 2, 3, 4, 5, 6,7],
Let U
S
:
'rI,
1, 3,6) and
T:
{1, 3' 4, 5}' List the elements ofthe
following sets'
ShT
Seiect the correct choice beiow and,
,:.:^ S hT:
-)+.
{il}
futt
a cornma lo separate answers as needed')
f.:"
The solution is the emPtY set'
LetD
:
{16,1g,21},B: {16,18,19,20}
List the elements in the set (D
(D
if necessary, fil1 in the answer box to complete your choice'
u E) .', F:
u
E)
n
and F
:
{I5'17'18'19'21}'
F'
t[]
List the eiements in order with no dupiicates')
(Use a coulma to separate answels as needed.
aa
M:
{a1i students taking
following set in words'
Let
calcuius} and P :
{a11
students taicing chemistry} ' Describe the
MUP
What is MUP?
il.:,
f::,'
who are taking calcuius or chemistr-y (or both)}
{all students in this school
calculus oI not taking chemishy or taking
students in this school who are not taking
{a1i
neither course)
i.i"{allstudentsinthisschoolwhoarenottakingcalcuiusandtakingchemistry}
36.
tl,r.
school who are taking calcuius and chemistry}
{al1 students in this
LetB
:
{a, b, c,
{e,f}eB
ij True
l: False
{a. \ e. f}
i-.:
:j-',
I(
}cB
True
Faise
e,flcB
'i
True
:
False
{d}, {e,
f}}.
Answer each ofthe following astrue or faise
.
37.
possibie set that
The table shows some trees that are in two city parks. Let u be the smaliest
the sel of rrees in
includes al1 the trees listed. R be the set of trees in Riverside Park, and S be
Sleepy Hollou' Parh. Find R'.
Riverside Park
Slee
Sycar-nore,
Oak, o
s
Cherry, c
Eim, e
Oak, o
Pine, p
Hollov, Park
Mapie, m
Sycamore, s
Dogwood, d
Cherry, c
Use the lowercase letters in the table to list the eiements in R
R': {n}
(Use a comma to separate answers as needed')
id.
Any or none of them
Arturo, Beau, Carlos, and Dean are four Senators On a certain subcommittee'
the new
for
variations
may be seiected to another subcommtttee. How many different
subcommittee are there?
There
39.
will be I
possible subcommittees.
The foiiowing sets are represented by diagrams. Choose a match'
a. Choose the set that matches the
Verur diagram on the nght.
-'
AuQ
l,:
Ar,Q'
A'nQ
A'uQ
b. Choose the set that matches the
Venn diagram on the right.
i.'
AuQ'
AnQ'
-.i
A
hQ'
(AnQ)'
c. Choose the set that matches the
Venn diagram on the right.
A,
Q,
o-A
A-Q
the set beiou'
Select the Venn diagam that represents
40.
BnA'
Choose the correct answer below
U
U
Which of the Venn diagrams represents the
following sets?
41
+1
")
PnQ (PnQ)'
PnQ' (PnQ)u(PnR)
b)
,\
dlrp..O)u(PnR)is
-'r'
represented b)' rn'hich
\/enn dtagraml
'-r
r.----:::!a:-:l
I
l-l+iTT*f-1ri i
lfP
I
--.,--i'p
irta)l,/l
l\ /.:)'
I ! n.r
I
I
\''J'
\'-"
I
I
I
I
'trQ#l
1.,
:l
l "i."*t,i' :l
1+--l
/r
l'. ,\r
l,'p
q tl
/
l''^;1
|
'*.2
I
I
is represented by which Verur diagram?
42.
use llle unlorl I uls
If n(A):
u B):
n(A
43.
12, n(B)
drlbwer
LU
:74
'
andn(A
n B):8'
what is n(A
u B)?
I
Use the union rule to answer the question'
Ifn(B):24,n(AnB):3andn(AuB):51'whatisn(A)?
n(A)
: l-l
(Simptify your ansu'er.)
Use the given information to frll in the number
of eiements for each region in the Venn
diaqram.
44
n(A):
n(A
18, n(B)
n B):
10,
=
x
z
n(B') :36
The number in Place of Y should
The-number in place-qlw g-lrould
l'--l
i
bt i
The number in Piace of z should be
45.
R
19
The number in piace of x should be
.
"LI I)',
I
i
i
I
bt l-J
B) :8, n(A) :23,
^
and n(A'u B') :76, determine the number of
Given that
n(A u B) :53, n(A
elements in each of the disjoint regions labeled with
Roman numerais in the Venn diagram to the right.
There ur.
i
46.
I
element(s) in region I,
I
eiement(s) in region
II,
-
eiement(s) in region
i element(s) in region IV.
Use the given information to fill in the numbers
of eiements for each region of the Venn
diagram.
Type the numbers that belong in the following
reglons.
i--l
\\/:l !lJ I T=l
I
Type the numbers that belong in the foliowing
regions.
l-_l-
n'.-'__)Jit'-:
Type the numbers that belong in the foliowing
regions.
m:i : n=; , P:i_,
I
n(An B n C)=4
n(C n B''):26
n(A'n B'n C'):
n(A n B): 12
n(A n C):1
n(B n C): 10
C') :21
-/R. rr tt\ -)A
n(a
n
10
III,
and
j
I
.
Suppose you drarn, a card from a well-shuttled decli ot
) i calos. f lno
eacn oI Ine
lolrowlng
probabiiities.
What is the probability of drawing a 9?
ll
(Srrnpiify your answet. Type a fraction.)
What is the probability of drawing a red card?
il
(Sirnpiify vour answer. Type a fraction.)
What is the probabiiity of drawing a biack king?
52.
li
You are dealt one card from a standard 52-card deck. Find the probabiiity of being dealt the ace of
diamonds.
The probabiiity of being dealt the ace of diamonds
53.
i. []
Suppose you draw a card ffom a well-shuffled deck of 52 cards. Find each of the following
probabiiities.
What is the probabiiity of drawi ng a 4 or u qu"en?
l-l
(Simpiify your answer. Type a fraction.)
What is the probability of drawing a diamond?
ll
(Simpiify your answer. Type a fraction.)
54.
A card is drawn from
well-shuffled deck of 52 cards. Find the probabiliq' that the card is a red
cardoraT.
The probabiiity is
55.
a
i-].
GVp. an integer or a simpli{ied fraction.)
A marble is seiected at random from a jar containing 6 red marbles, 4 yellou' marbles, and 5 green
marbles.
What is the probability that the marble is red?
S4rat is the probabiiiry ittu, the marble is r"d:
j6.
-
A marble is selected at random from a jar containing 3 red marbles. 2 yeilorn marbles, and 4 green
marbles. Find the probabiiity that 1t is the following.
a) the marbie is ttot yeltou'
b) the marble is either red or gteen
What is tiie probabilib,that the marbie is not yellorn'?
[
(Siinplifl')i our answer' Type a fraction')
What is the probabiiity that the marbie is red or gr"er,?
(Simplifu your answer. Type a fiaction.)
[l
60 fish The table belorn'
a d'a1''3 fishing' They caught a total of
Several friends chartered a boat for
qrp" uniorr-ber.-of fish caught' Determine the empirical
51
provides information
"1"*1rt"caught is a kingfish'
irobability that the next fish
Fish
Number caught
Grouper
l3
Shark
14
Flounder
2
tr3ngf,rsh
3i
P(kingfish):
yoularsw.et rwe
a ft;actlon )
llt-rltry
A fajr die is rolled, Find the following Probabilities'
i!
The probabiiity that the ro11 is a 4 or 6
l-l
is
'
except 3 is
The probability of getting any number
59.
:
1--J
and 8 biack marbles' If
A bag contains 2 white, 3 orange, 5 yeilow,
find the following Probabiiities'
The probabiirty of getting an orange marble
it L-l'
The probabiiity of not getting a biack marble
i' I
'
' :"
'i'"":r:
a
marbie is drawn at random'
1:'i'i"ii:
ii:
ANSWERS
1.
the second choice
8.
the fourth chotce
the first choice
the second choice
1a
lJ.
T
.F
I
F
F
A
1
-....;.."".-...... ........
C
tA
T
T
F
J.
F
15.
the
first choice
the secoad
4.
thoice
S
b
c)
D
i6.
A
B
5.
B
the second choice
t0,
6.
A
B
11.
the first choice
ll.
C
B
B
true
72
-n
m
m
-n
..^- ".
18.
19
A
20
C
21,
B
-.r
6
st6
-5
l.
1
C
22.
the second choice
39.
1
the second choice
the third choice
the third choice
2
1
26
the trrst chorce
-J.
40.
1
1A
-4.
52
the second choice
41.
D
D
53
C
2s.
the second choice
l3
B
1
.44
+L-
26.
2
4
18
the first choice
7
AL
27.
the second choice
the first choice
the second choice
t3
30
55.
z
)
44,
10
1a
Ll)
the second choice
9
28
10
the second choice
the first choice
the first choice
the second choice
.4<
56.
-|
g
7
l5
I
9
30
31
51.
31
60
30.
16
46,
4
10
I
J1,
A
58,
3
J
:
6
6
13
7:-
1:
18
70,I2:,13,74,15
59.
l
6
a 45
47.
the first choice
5
0
J+.
18,79,21
+o^o
4A
32
5
af
J -).
49.
5
6
29
36.
the first choice
the first choice
the second choice
14
14
50.
31.
mrd
5
6