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Math 102
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Test2-Chapters
1. Identify the statementas simple, compound,or neither. (1 pt/problem)
a. The car is in the garageand the bicycle is in the driveway.
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b. The teamleaderhasdecidedto takea vacation.
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c. You don't setto so to theTwin Citiesthisweek.
d. Nobodygoesto that restaurant,it's too crowdea.
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e, Jessicawanted to attend the meeting, but she had to go to class.
2.Writetheset{xe Integer
notation.1rrr"1{..:3 ,- )r-\P , . - 6
I x < 7} in roster
3. Findthecardinal
numberof thesetM: tt, U,n,
..., 462\. (2pts)
,t?,trt,
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4. Whatis thenextnumberin thesequence
l,1,2,3, 5,'8,
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5. Fill in the blanks with one of the following €r G, c
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to make each statementtrue. (l pt/problem)
6. Illustrate each of the following set notationsby shadine the Venn diagramsbelow: (2 pts/problem).
b. (r u M)-o
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7. Use set notation to describethe shadedregion. @pts)
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8. Usea truth tableto determineif the whetherthe argumentis valid or invatffi;
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" t Lcontgn t-rt.
If t@e,
thentheponddo"r ngt
If thj:po"d does rlqt
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a1d do-_1s_not
coltain trollt, then the pond does not contain frogs.
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Thepondcontainsaleae.
Therefore,the pondcontainsfrogs.
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9. Rewrite the statementin the form "ifp, then q" . (2 pts/problem)
a. To run a marathon it is necessarythat you train very hard and long.
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b. I will loseweightif I diet.
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10.If A e+ B is true andB is false.thenA is fi
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ll . If q it: fbfS; r is true,ands is true,thenthetruth valueof the following ir'(ro* yourworkforz ptf
(q v -r)
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12.A surveyof 220 families showedthat:
83 had a dog;
64had a cat:
28had a dog and a cat;
84 had neither a cat nor a dog nor a parakeet;
6 had a cat, a dog, and a parakeet.
11.
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a. Use a Venn diagram to representthis information. (2pts)
b. How many had a parakeetonly? (t pts)
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13. Construct a truth table for (q -
, 4s
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-r) <+ q A- r .
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punctuation
. (3pts)
intowordswith appropriate
thestatement
to translate
14.Usethefollowingdefinitions
p: Themonitoris included.
q:Tl;recolorprinteris optional.
r: Thejump drive is exffa.
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15. Use DeMorqan's law to createequivalentstatementsfor each of the following. (2 pts/prob)
a. -(-P n a)
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b. You werei11,or ysgl{gsllqglass.
(Write usingsymbols,applythe law, andthentranslatetackto words
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16. Re-write the argument to the right on a single line and
number the connectivesin the order they are to be evaluated.(l pts) p ^- q
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: . q Yp
17. Match the following argumentswith their name.(Not all nameswill be used1 pVproblem)
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p -+r
-1C Conditional to Disjunction
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:,-p
A
B. Fallacy of the Inverse
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p+q=-pvq
d Dislunctive Syllogism
,il,fanacy
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of the Converse
E. Law of Syllogism
p: Law of Contraposition
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$ Law of Detachment
18. Use an Euler diaeram to determinewhether the syllogism is valid. (3 pts/problem)
a. Somestudentswork full-time.
All full-time workersget earnvacation.
.'. Some studentsearn vacation.
b . All business€s
aresubjectto safetyinspections.
This restaurantis subjectto safetyinspections.
.'. This restaurant
is a business.
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19. Tell whether each statementis true or false, if false explain why (2pts/problem).
a. The negation of "Some of my studentsare doing excellent" is "Some of my studentsare
not doing excellent."
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b. The following are lo
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/ fwZc. The statements:"If it is cold outside,thenyou light the fireplace."and "If you light the
fireplace,thenit is cold outside."areequivalent.
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d. The form of the argumentbelowis Ljyfl!y'lggism which makesit valid.
If I'm hungry, then I will eat.
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- - - - - - - -Therefore,I will not.eat
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e. The statement:"The warrantv is void if the car has
gver 3 yqarsold." Is an exampleof the exclusiveor.
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properly maintained or it is
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20. Write the inverse statementfor the following: (2pts)
You did not huu" classthis Monday, only if it was the week after July 4th.
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21. Use inductive ..uril-ing ,o determinethe units digit of 720.(sdo* yourworkfor 3 pts)
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is valid or invalid'
rf the
a truth tableor write a proof to determine
22. Comple,te
'5pn lgument
andp: I passmath'
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Let g: I will graduate,
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I will graduateif andonly if I passmath
! graduated.
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23. constructa,,formalproof,to estabrish
followingargumentis valid' (4 pts)
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