Math 102 Test 2-Chapters | &2, Schemes and Mind Maps of Law

Download Math 102 Test 2-Chapters | &2 and more Schemes and Mind Maps Law in PDF only on Docsity! Name Math 102 Test 2-Chapters | &2 1. Identify the statement as simple, compound, or neither. (1 pt/problem) a. The car is in the garage and the bicycle is in the driveway. C-"-"^ p.l--S b. The team leader has decided to take a vacation. 5,l"Wt9- '' r c. You don't set to so to the Twin Cities this week. &l^,t7.r-.-^g d. Nobody goes to that restaurant, it's too crowdea. N e-l t-Lt.gf (?^.r ^ /" V ) e, Jessica wanted to attend the meeting, but she had to go to class. 2. Write the set {xe Integer I x < 7} in roster notation. 1rrr"1 {..:3 ,- )r-\P , . - 6 3. Find the cardinal number of the set M: tt, U, n, ,t?,trt, ..., 462\. (2 pts) 3w 3 t5+ i 9 . A , 4. What is the next number in the sequence l,1,2,3, 5,'8, F, ^l . (2 pts)' \ / 5. Fill in the blanks with one of the following €r G, c to make each statement true. (l pt/problem) 6. Illustrate each of the following set notations by shadine the Venn diagrams below: (2 pts/problem). b. (r u M)-o U %- sru 5*-{ 6 =/ J V I r - - 7. Use set notation to describe the shaded region. @pts) , :K-A ^ lo{ BnP' o{ nrA-,[ 8. Use a truth table to determine if the whether the argument is valid or invatffi; c \ " tL , If t@e, then the pond do"r ngt contgn t-rt. - n \ If thj:po"d does rlqt "o"tui a1d do-_1s_not c ltain trollt, then the pond does not contain frogs. The pond contains aleae. Therefore, the pond contains frogs. \y . It r^ J ,Ltt a I +k* SLrU{Cn;Jr) \90i ilS $ T T t- r ( F E -v r ( a t trr 1'T 1' T I Ir r i F i: r F F r a F T T,r* -T F T T I-( T -t-Y1 T F TT'a-T T F B _9 T -ra 1 Ctr -r T 1 1r(Q; F T T {t r- T aFI1tr FtrrT rr T F T-* t*- I F T l-" .rt I _ t I F 1 T A T T T TA F tr T I- I ,f,l ' til 4- zr, a ' 5 z r - l L ( - o ^ - € ) : - { z d - ! - - r - + I 8 . Iv"fJ :' 16. Re-write the argument to the right on a single line and number the connectives in the order they are to be evaluated. (l pts) p ^-q __p__ : . q Y p 17. Match the following arguments with their name. (Not all names will be used 1 pVproblem) iF -1C Conditional to Disjunction B. Fallacy of the Inverse d Dislunctive Syllogism ,il,fanacy of the Converse p v ( l -p :. ql p -q l __q ___ : . p 18. Use an Euler diaeram to determine whether the syllogism is valid. (3 pts/problem) a. Some students work full-time. All full-time workers get earn vacation. .'. Some students earn vacation. All business€s are subject o safety inspections. This restaurant is subject o safety inspections. .'. This restaurant is a business. A t l ft p -+ r __7 r_ : :,-p p+q= -pvql l . l l l . lV. _) E. Law of Syllogism p: Law of Contraposition $ Law of Detachment b. b. Tl-g 5I^J"+y\ @4 Keil.o.*ra.^rl-- f,,/^)u$ 19. Tell whether each statement is true or false, if false explain why (2 pts/problem). a. The negation of "Some of my students are doing excellent" is "Some of my students are not doing excellent." [ist d^* ."(---ruil_ &*X, u-llg j b. The following are lo < *vnLilv,# --<- / fwZ- c. The statements: "If it is cold outside, then you light the fireplace." and "If you light the fireplace, then it is cold outside." are equivalent. 7 - / \ n A l -cLJLs< I+ &o i p/,$ +{*1: G,*p\..s N tr$^<-r1 o $ {-}\. Co-r,+er<-e I d. The form of the argumentbelow is Ljyfl!y'lggism which makes it valid. If I'm hungry, then I will eat. - -ln go-t-bgt-gyi - - - - - - - - - Therefore, I will not.eat r*tl 51,,0-e*-1r L?. r v\o{ 4"> y eqtrivalent dv e and e v d. . , t-t._-o LnUu e. The statement: "The warrantv is void if the car has properly maintained or it is gver 3 yqars old." Is an example of the exclusive or. -'i- t 4 n ( , l u . r 5 r l ' ( _ , lO t 20. Write the inverse statement for the following: (2 pts) You did not huu" class this Monday, only if it was the week after July 4th. ---.- l' l l I t ou\ '"1, t r - n l-oJSs 1- A l4-Ysp tJ'-(>') +.1' '/'i\*" #-n" t+ vrr/.: i"+--1-|, wu-)L ^{\r-i SJ,\ 4t't ' q 21. Use inductive ..uril-ing ,o determine the units digit of 720. (sdo* your work for 3 pts) q)-r i f ' f qe = Aq 1r \ .13 -\+3 4 ..' {-- r 4o (t -+- 1t5- 1'rJ, ' ," i ,.| , t,i ! :"i,. in 4c{ q Jo ,'o-, a\5 +=vJ L2t . -'' ,4 -r , / l \ / \ J 22. Comple,te a truth table or write a proof to determine rf the lgument is valid or invalid' Let g: I will graduate, andp: I pass math' / '5pn I I will graduate if and only if I pass math ! graduated. ffr"t"f"t., I Pasied math' T ; I ( 1 / T I I ; . Y l ' (T r l rr f lt-r { r- l ' 1 Y 1 f { l' Y 22. o.J 23. construct a,,formal proof,to estabrish that the following argument is valid' (4 pts) v' -q -q -+ ( r rq ) --aA,5d"\ 5 Jr e-^\lo' ; . r F^ito \) ̂ 'tt(.uil N \V I \ ^q el* ) h r l 5\ .u \ Ar Lad^l@$ttl \ D.s \,,w\A\'a- tl \rttl**Jd t-? ,4