Sets and Relations Questions and Answers

WAL A normal distribution has a mean of 12 and a standard deviation of 3 Use the 68 95 99 7 rule to find the percentage of values in the distribution between 12 and 18 What is the percentage of values in the distribution between 12 and 18 KRIEB

V8 5 07 V1 D VA E 05 F U6 G t 06 So 07 H 08 1 None of the above U5 V3 3 Let S 1 04 08 Which of the following vertices are in N S A 1 B 02 C v3 VA Note In order to get credit for this problem all answers must be correct

4 of local services are charged to property owners by municipalities to pay for a number

1 point a Consider the relation R on the set A X Y Z defined by R X Y X Z Y X Y Z Z X Z Y This relation is not reflexive What element s would we need to add to R in order for it to be reflexive b Consider the relation R on the set A X Y Z defined by R X X X Y X Z Y Y Y Z Z X This relation is not symmetric What element s would we need to add to R in order for it to be symmetric c Consider the relation R on the set A X Y Z defined by R X Y Y X Z Z This relation is not transitive What element s would we need to add to R in order for it to be transitive

12 Given the following Venn diagram where each area is labeled by three binary digits which one of the following represents the area 111 000 O AUB C O ANB nC O AUB C A 100 101 110 111 001 010 011 C B U

15 Let A and B be two subsets of the universal set U Which of the following is equivalent to An BUA O An B 0 0 O AUB O None of these answers

6 Let S be a set Which of one of the following is always correct O a E Simplies a P S O a ES and b E Simplies a b P S a ES and b E S implies a b P S OaESand b E Simplies a b S

11 If the universal set U a c b d e f g h i j k l m n o p and A is a set of vowels in the word home then A is O a b c d f g h i j k l m n p O c b d f g h j k l m n p O e o None of these answers

5 Given the set S 1 2 4 8 16 1024 which one of the following sets represents S using the rule of inclusion 2n ne Z and 0 n 10 O 2n ne Z and 0 n 11 O n ne Z and 0 n 10 2n ne Z and 0 n 10

2 Which of the following is a subset of b c d O b c d O 1 2 3 O a b c O a

1 Let S 1 2 3 1 2 3 What is the cardinality of S

In this problem we prove the following statement Let A B be sets in a universe U Then A n BC AUB Your task is to provide justification for some of the steps Possible answers are given below Put a number into each blank with no parentheses 1 definition of union 2 definition of intersection 3 definition of subset 4 definition of set subtraction i e S T 5 definition of complement 6 DeMorgan s law of logic Proof Let a An B Then x EA and a E B by justification 2 Since a A this means that a A by justification 5 Using the same reasoning a E B means that a B so x B is true Combining these facts x E A A B is true Therefore EA V E B is true using justification 6 In other words E AUB is true using justification 4 Since AUB this means that a AUB using justification 3 This concludes the proof that ABC AUB D So EA is true which is equivalent to a AUB

Let T D R be sets contained in a universe U a Using the distributive law which of the following is equal to the set TU DNR OA TUD n DURC OB TND U TOR OC TUD n R OD TUD n TUR OE None of the above b Using the DeMorgan s law which of the following is equal to the set TU D n R OA TU DNR OB TU DUR OC TUD n R OD TUD U TUR

Suppose that R C are sets so that RC C Also let tERand z E C Which of the following statements must be true OA te C OB z t E C x R OC t z E R x C OD ZER A

This problem covers more laws of set theory Let B be a set contained in a universe U Each set below is equal to B or U Select the correct set from the drop down menu Try using a Venn diagram if the answer isn t immediately clear Involution Law B Null Laws BUU Bn Idempotent Laws BUB BnB Identity Laws BU BOU Complement Laws BUB

Directions Complete the follow providin formula booklet Round to 3 s f if not otherwise specified Six restaurant locations labelled A B C D E and F are shown together with their Voronoi diagram All distances are measured in kilometres 8 7 6 4 C

1 point If a i j 4k and b i j 5k Compute the cross product a x b axb i j Note You can earn partial credit on this problem

Two functions fand g are defined in the figure below Domain of f 7 Range of f Domain of g 00 Range of g Find the domain and range of the composition g of Write your answers in set notatic a Domain of g of 0 b Range of g of 0 0 X 0 0 G

Domain h Function Not a function Relation 1 Function Not a function Relation 3 Domain Range j e n d f sun sun sun sun sun Range 2 8 7 3 6 Domain O Function O Not a function Relation 2 Relation 4 Domain Range 6 2 4 0 Function Not a function 3 7 6 3 6 0 Range S a b

pictogram shows the favourite chocolate of a group of students The number who chose snickers twix have not yet been included Use the clues below to complete the pictogram and the key Wispa OOP Snickers Clues A 26 students said either wispa or bounty B 36 students said snickers C 72 students took part in the survey Twix Bounty D key O 11

12 Which statement is true Give an example to justify your choice a All functions are relations but not all relations are functions b All relations are functions but not all functions are relations

Determine whether the statement is true or false and explain why In a Venn diagram draw one circle for A and a second circle for its complement Choose the correct answer below CTLED O Points 0 of 1 OA The statement is false The complement is the universal set outside of the circle for A OB The statement is true This statement applies to all Venn diagrams OC The statement is false The complement is the region where the circle for A and the second circle overlap as well as the universal set outside of both OD The statement is false The complement is the region where the circle for A and the second circle oversp

Which substance s belong in the products box Choose all that apply A N B 0 C H O D SO E Fe O3 F Fe OH 3 12

Noah puts 3 57 grams of blueberries in his oatmeal and feeds his bird 1 3 grams of blueberries How many grams of blueberries does Noah use altogether

Consider the proposition over Z2 given by g x y x y x y That is the variables and y take integer values Put a checkmark next to those propositions which are true OA VI y q x y B q 1 1 OC Ey q 1 y OD 32 3y q z y E V Vy q z y DE 3r Vyg z y

ic 6 3 Conduct a test of Ho p2 2 3 versus Ha 2 3 for the sample data summarized here Use a 01 in reaching your conclusions Sample size Sample mean Sample standard deviation Population 1 13 50 3 7 23 2 21 58 6 6 98

6 2 asic Inferences About Independent Samples 6 2 For each of the situations set up the rejection region a Ho 2 versus Ha b Ho MM2 3 versus Ha c Ho M2 9 versus Ha 2 with n 12 n 15 and a 05 2 3 with n n 25 and a 01 2 9 with n 13 n 15 and a 0

List all the ways to select two different members from S with repetition The order in which members are selected is important For example AA is allowed and AB is not the same selection as BA S D E F G H Identify the list of all the ways to select two members from S Choose the correct answer below O A DD DE DF DG DH EF EG EH FG FH GH OB DF DG DH EF EG EH FG FH OC DD DE DF DG DH EE EF EG EH FF FG FH GG GH HH OD DD DE DF DG DH ED EE EF EG EH FD FE FF FG FH GD GE GF GG GH HD HE HF HG HH

Which of the following are tautologies Select all that apply OA p 0 OB p q p OC p pVq OD q p q p OE pVq OF p p q q

Consider the following statement If Jane has taken chemistry then Jane has taken biology a Which of the following statements is the converse of the given statement OA If Jane has not taken chemistry then Jane has not taken biology OB If Jane has taken biology then Jane has taken chemistry OC If Jane has taken chemistry then Jane has not taken biology OD If Jane has not taken biology then Jane has not taken chemistry OE None of the above b Which of the following statements is the contrapositive of the given statement OA If Jane has not taken biology then Jane has not taken chemistry OB If Jane has not taken biology then Jane has taken chemistry OC If Jane has not taken chemistry then Jane has not taken biology OD If Jane has taken biology then Jane has taken chemistry OF None of the above

The editors of Auto Web have evaluated several E uropean and J apanese crossovers and given them either a H igh or A verage safety rating The probability tree to the right summarizes the results of the study If a car from the study is selected randomly find the probability P A P A TUR 0 40 E 0 55 H 0 60 J 0 45 A 0 75 H 0 25 A

The Political Action Club has surveyed 270 students on your campus regarding the relationship between their political affiliation and their preference in the 2016 presidential election The results are given in the following table Republican 23 87 110 Totals 151 119 270 Democrat Independent 22 Preferred Candidate A Preferred Candidate B 106 17 123 15 Totals 37 If a student is selected randomly from those surveyed find the probability that the student is an Independent given that the student preferred candidate B The probability is Type an integer or decimal rounded to three decimal places as needed RECERR

According to U S government statistics mononucleosis mono is four times more common among college students than the rest of the population Blood tests for the disease are not 100 accurate Assume that the following table of data was obtained regarding students who came to a certain school s health center complaining of tiredness a sore throat and slight fever Has Mono 45 12 57 Doesn t Have Mono 26 10 36 Totals 71 22 93 Positive Blood Test Negative Blood Test Totals If a student is selected from this group find the probability a student doesn t have mono given that the test is negative The probability is Type an integer or decimal rounded to three decimal places as needed

In a certain game you roll two 4 sided dice to determine the number of spaces to move a game piece clockwise around the board Assume your game piece is on the square marked X What is the probability that you will land on a shaded square on the next move The probability is Simplify your answer X

850 mb Maps The 850 mb map provides a view of the atmosphere above the boundary layer where diurnal temperatures are strongly influenced by warming and cooling of Earth s surface The 850 mb chart includes raw data at each station height contours and isotherms Figure 9 15 Meteorologists use the 850 mb layer to find areas influenced by the movement of warm and cold air masses Warm air advection exists when winds blow across isotherms from warmer to colder areas cold air advection occurs where winds blow across isotherms from colder to warmer areas During the winter months information on an 850 mb map can help forecasters determine the likely form of precipitation Forecasters often look at the 0 C isotherm at 850 mb as the division between snow and rain 1380 1380 1410 1440 1410 1470 1500 10 L 1516 10 H 1528 1410 1380 1350 H 1534 1530 1320 H 1538 10 What range of heights do you see in this example of the 850 mb surface 11 Circle and label areas of warm and cold air advection on the 850 mb map 12 Highlight the 0 C isotherm 1320 1350 1380 1410 1440 1260 1320 1290 1230 1350 1530 Figure 9 15 An 850 mb map 1560 1470 H 1612 10 10 1590 1500 1590 1530 0 1560

A 7 10 n AUB n Anc n An BnC Determine the following cardinalities n A 20 n AUBUC n A n BnC gram shown below 6 12 5 B

In 2019 Chen Corporation purchased treasury stock with a cost of 49 000 During the year the company declared and paid dividends of 8000 and issued bonds payable for 1 100 000 Net cash provided by financing activities for 2019 is A 1 051 000 B 1 100 000 C 1 043 000 D 1 092 000

Q7 For each of the following functions try to prove that they are continuous at zo Otherwise show say why they are discontinuous 15pts If All correst 1 a f z 23 1 1 1 b f z Arg z i z 1 z 1 zo i zo i

The following table presents the number of reports of graffiti in each of New York s five boroughs over a one year period These reports were classified as bei open closed or pending A graffiti report is selected at random Compute the following probabilities Round final answer to four decimal places Part 1 of 6 Borough Bronx Brooklyn Manhattan Part 2 of 6 Queens Staten Island Total Source NYC OpenData a The report is open and comes from Manhattan The probability that the report is and comes from Manhattan is b The report is closed or comes from Queens Open Closed Pending Total Reports Reports Reports 1121 1622 80 1170 2706 744 3380 1353 2043 83 118 4471 9869 Send data to Excel 0513 X 48 25 25 0 178 2823 3924 4149 3421 201 14 518 3

You are buying a triple deck ice cream cone with peach vanilla fudge berry and mocha as possible flavors The flavors can be repeated or not and two cones are considered to be different if th flavors are the same but occur in different order How many possible cones have only peach and fudge scoops cones Type a whole number

Let S 1 2 12 a How many subsets B of the set S satisfy the property that 1 2 CB Answer b How many subsets B of the set S satisfy the property that 1 2 3 4 B Answer

For each positive integer i let S be the following set Si i i 1 i 2 2i 1 That is S is the set of integers between i and 2i 1 inclusive For example S8 8 9 10 17 Also let T 1 3 5 7 Compute the following sets 3 a US j 1 5 b Sk k 3 5 c U SinT i 2 d Tn US i 2

Next list all the members of AUB n C MY NOTES Let U 2 3 4 5 6 7 8 A 2 3 4 5 B 2 3 6 7 and C 4 6 8 Consider the following set Enter your answers as comma separated lists AUB nC First list all the members of AUB Then list all the members of AUB n C ASK YOU

Let U 1 2 3 4 5 6 7 B 1 3 5 6 and C 4 5 7 List all the members of the given set Enter your answers as a comma separated list Enter EMPTY for the empty set BUC

Consider the given set operation Let U 1 2 3 4 5 6 7 8 9 10 Enter your answers as a comma separated list Enter EMPTY for the empty se x x is a multiple of 2 U x x is a multiple of 3 Identify the elements in each set x x is a multiple of 2 x x is a multiple of 3 Perform the given set operation

Let U 1 2 3 4 5 6 7 and A 1 2 3 4 List all the members of the given set Enter your answers as a comma separated list Enter EMPTY for the empty set A

Perform the given set operation Let U 1 2 3 4 5 6 7 8 9 10 Enter your answers as a comma separated list Enter EMPTY for the empty set a 1 3 6 n 8 10 b 1 3 6 U 8 10 c 1 3 6 8 10

4 1 point The volume of this cylinder is 900 m Determine the height of the cylinder to two decimal places d 12 4 m C 1 86 m b 9 3 m 7 45 m 12 4 m d 5 59 m

1 Is the following sequence convergent or divergent 3 2n 5n 3n 2 An O Converges to 0 O Converges to 2 3 O Diverges Converges to 5 2

1 Absolute Location Vocabulary Unit Basics of Geography Define the following key terms 2 Cartography 3 Geography 4 Latitude 5 Longitude 6 Mercator Projection 7 Polar Projection 8 Political Map 9 Physical Map 10 Relative Location