ANSWE2 k?
Math 106, Practice problems on set cardinality
r- i'L u 2008
1. A survey of 75 students was taken, asking whether the student had slept less than 4 hours any
one night in the past week and whether the student had a GPA of at least a 2.5. Of rhe 75
students, 30 had slept less than 4 hours in on^e night (set S/ ; 55 had a GPA of at least 2.5 (set
G),and 20 had both slept less than 4 hours arid had at least a 2.5 GpA.
a) Use the Venn diagram below and deterniine the cardinality of each region:
6(S):3O
., (c) = 55
,', 15 66): ZO
ntsuc): n LS) +n t c')- n(S ne)
- 10 + 5s'.-2O ' bS
n ts va)' = n (-?,t\- n (s u c)
a-1 S-(,fala
U
b) How many students slept less than 4 hours o; had a GPA of at least 2.5? n ( s u{')
L 5 s'v. 1.'xiJ
c) How many students did not sleep less than j hours agl had qGPA of less tUaul-lS
"^(:'13_)_:_:_e__i:!_!j,,t: r , ,:a.v,1trte,-i ,*W'll dJt l
n (suc')' ;
(tr,ttur6a*t@) d) How many students had a GPA of at least 2.5 and did not sleep less thanj
hours? e5.s- ' = ; '-r A --' -, .-,(GoJr)
( tn k, not,rrr S)
A survey of 98 students was conducted, asking whether the student lived on campus and
whether the student owned a car. Of the 98 studerrts,47 lived on campus (Set I); 68 owned a
car (Set C), and 13 did not live on campus and did not own a car.
a) Use the Venn diagram below and determine the cardinality of each region:
2.
L'ne')='", (uuc)'-- tJ 1t. n(vvc)113',
n ( t-)' *l
n (c), b9
n(
, ^(tvurtna*i
Lat)
v
(nok: n(X)' n(uurc-)+
n(uuc)'8s)
9n3c dtr i,.-\wrrchnt: n( ;nc): alQ
n{ur,tc)' --n(u'nc')
rr ( uuc )',- so
+n(c)- n(uuc)=
+L9-8s- t 3O
b) Howmanystudentslivedoncampusq4downed acar? nluAc) : 3a sFydr"rF
n
c) How many students lived on campus but did not own acar? l-? Sh,^1c"ttj
,;i".':''/'/"':-
d) How many students lived on campus o_r owned a car?
n( r- ..r1)
g 5 sfrr/rrrff
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