Sets and Relations Questions and Answers

Let f 4 5 7 7 11 13 be a bijection Which of the following statements must be true Select all that apply DA fof 13 13 OB fo f is the identity function on the set 7 11 13 OC f of is the identity function on the set 4 5 7 OD f f 7 7 DE f of is the identity function on the set 7 11 13 OF fo f is the identity function on the set 4 5 7

Which of the following functions are surjective Select all that apply OA f 2 3 7 12 2 11 17 defined by f 2 11 f 3 11 f 7 2 f 12 17 OB f 6 8 9 13 2 3 7 12 defined by f 6 12 f 8 3 f 9 7 f 13 3 OC f 2 3 7 6 8 9 13 defined by f 2 13 f 3 8 f 7 9 OD f 6 8 9 13 2 3 7 12 defined by f 6 12 f 8 3 f 9 7 f 13 2

Let S 1 5 11 17 and T 4 2 8 14 Which of the following are functions from S into T Select all that apply DA 5 8 11 14 17 4 1 2 OB 1 14 5 4 11 8 1 2 OC 1 14 5 14 11 2 17 2 OD 1 4 5 2 11 8

This is a strong positive correlation between the number of corrections assignments completed and the overall course grade in this class The line of best fit is given by y 15 4z 6 where x is the number of corrections assignments completed and y is the overall course grade Suppose someone completes 6 correction assignments What can you predict for their overall course grade When 6 corrections assignments are completed I can predict the overall course grade will be

Letr be the following relation on the set Z cry if and only if y x 2 Which of the following are elements of r Select all that apply OA 10 4 OB 2 4 OC 5 9 OD 5 1

The definition of transitive may be restated as follows Definition Let r be a relation on A Then r is transitive if and only if whenever a b er and b c Er it must be true that a c Er Let A 2 3 6 10 14 Let r be the following relation on the set A r 2 2 2 6 3 14 6 2 6 6 14 10 a Find all the elements in r2 Enter your answer below as a list of ordered pairs separated by commas Answer 4 b List all ordered pairs that are in r2 but not in r Answer c The relation r is not transitive Explain why not by filling in the following blanks with the appropriate ordered pairs Answer r is not transitive because is in r and is in r but is not in r

Let A 2 4 6 Define r to be the relation on the set A defined by the following xry if and only x y 2 Enter each answer below as a list of ordered pairs separated by commas a Find all the elements in r Answer r b Find all the elements in r

A candy jar contains 10 red jelly beans 9 yellow jelly beans 8 pink jelly beans 7 black jelly beans and 6 green jelly beans SHOW YOUR WORK 9 What is the probability of pulling a green jelly been out 10 What is the probability of pulling a green one out and THEN pulling a green or red one out don t forget once you pull the first green one out your sample size has decreased by one

K Use the Venn diagram to determine whether the statements are equal for all sets A and B A UB and A U B Are the statements equal for all sets A and B O O Yes No CHE This question 1 point s possible A 100 I II U IV B II

K In the universal set U a b c h define subsets of cars with the characteristics shown to the right Describe the following set in words and then find the set POC 0 Click on the icon to view the table of new car features Define the set PnC in words Choose the correct answer below OA The set is the set of cars that cost more than 20 000 and are not compact OB The set is the set of cars that both cost more than 20 000 and are compact OC The set is the set of cars that either cost more than 20 000 or are compact OD The set is the set of cars that cost 20 000 or less and are not compact Identify the elements of the set Pn C Select all that apply A g C h E d G e 1 1 PnC is the empty set P price is above 20 000 C is compact G A has a good safety rating has antitheft package W warranty is at least three years B b D c F f H a Data table Car a b C d T e f g h Cost 23 000 16 500 21 600 21 000 20 400 18 900 18 100 23 800 poss Size midrange subcompact compact compact compact subcompact subcompact midrange Print Warranty years 3 2 3 3 2 3 4 4 Done Sat

Use the following table of electives to describe the set below in an alternative way World Culture Cultural Diversity Humanities No Yes Yes Yes No Writing No Yes Yes Yes No Yes No Class A Class B Class C Class D Class E Class F Yes Class G Yes Class B Class C Class D Class F Class G Choose the correct answer below OA x x is a world culture elective OB x x is a writing elective OC x x is a humanities elective OD x x is a cultural diversity elective Yes Yes No No Yes Yes No No Yes Yes No No Yes Yes

Find the inverse of each matrix if it exists 6 3 5 7 3 32 2 G 34 6 3 8 Use a matrix equation to solve each system of equations 9 2x y 9 x y 3 10 4x 2y 22 6x 9y 3 2 1 2 0 K 3 L 21 0 4 01 1 11 12 MONEY Kevin had 29 quarters and dimes The total value of all the coins was 4 70 How many quarters and dimes did Kevin have Problem Solving xhium instilleos termine whether each pair of matrices are inverses of each other 14 M 11 2x y 4 3x y 1 16 R boss 1 3 N 11 0 2 4 5 0 Extra P s 4 2 2 S 4 2

Pandora com surveyed a group of subscribers regarding which online music channels they use on a regular basis The following information summarizes their answers 7 listened to rap heavy metal and alternative rock 10 listened to rap and heavy metal 13 listened to heavy metal and alternative rock 12 listened to rap and alternative rock 17 listened to rap 24 listened to heavy metal 22 listened to alternative rock 9 listened to none of these three channels a How many people were surveyed b How many people listened to either rap or alternative rock c How many listened to heavy metal only

work 3 3 Complete the truth table for the given statement by filling in the required columns qvp pq TT TF FT FF Complete the truth table P T 9 q T q qvp qV p Question 8 3 3 22 Part 1 of 4 qvp q vp

Use the table to answer the question Consider the set V GPA above 2 0 Which set is equivalent to but not equal to V Choose the set equivalent to V but not equal to V OA Dana Brenda Elston Carmen Frank Gina OB Dana Brenda Carmen Gina O C Dana Elston Frank Gina OD Dana Elston Carmen This question 1 point s possible 33 Submit quiz Major Class Rank GPA Activi Dana History Junior 3 9 Band Brenda Math Senior Elston Business Freshmen Carmen English Senior Frank History Junior Gina Business Junior 1 8 Yearb 2 4 Baseb 1 7 Socce 3 7 Tennis 3 7 Choir

Assignment 4 8 points Find a minimum spanning tree for the following graphs and Prim s algorithm G G2 3 11 3 3 2 4 15 10 5 12 4 3 4 2 13 5 2 4 1 6 9 7 14 3 5 6 7 ing

K The accompanying table gives nutritional information for the following fast food items Monster m Monster with Cheese mc Bacon Cheeseburger bc Hamburger h Cheeseburger c Fish Sandwich fs and Ham Cheesy hc Find the set PUCUB Identify the elements of the set PUCUB Select all that apply A fs C c E mc G hc Data table Item m mc bc h C fs hc Protein 38 51 47 39 23 28 27 of Minimum Daily Allowance MDA Vitamin A Vitamin B1 12 27 10 21 21 28 15 44 6 0 11 12 18 18 P x x is an item that provides at least 30 of the MDA for protein C x x is an item that provides at least 10 of the MDA for calcium B x x is an item that provides at least 25 of the MDA for vitamin B1 A x x is an item that provides at least 15 of the MDA for vitamin A COLLE B m D bc F H PUCU B is the empty set h Calcium 8 19 20 26 4 6 12 X

K In the set of the ten top grossing movies of all time shown in the table available below define the sets as shown below M the set of movies that earned more than 1 5 billion L the set of movies that earned less than 2 billion the set of movies that were made before 2015 B Describe the set L M U B in words and then find the set Describe the set L M U B in words Choose the correct answer below C OA The set of movies that earned more than 2 billion or earned less than 1 5 billion or were made before 2015 B The set of movies that earned less than 2 billion that did not earn more than 1 5 billion or were not made before 2015 C The set of movies that earned less than 2 billion that did not earn less than 1 5 billion or were made before 2015 D The set of movies that earned less than 2 billion that did not earn more than 1 5 billion or were made before 2015 Identify the elements of the set L M U B Type the letter s of the movie s that is are in the specified set For example an answer could be B a b d g h i L M U B Use a comma to separate answers as needed Table of the Ten Top Grossing Movies Movie Movie a Movie b Movie c Movie d Movie e Movie f Movie g Movie h Year 2002 2001 2015 2008 2015 2015 2006 1992 Gross billions 2 5 2 3 1 8 1 5 1 4 1 4 1 3 13

The following Venn diagram represents Some S are not P True O False S X No answer text provided No answer text provided P

A small publishing company is planning to publish a new book Let C be the total cost of publishing the book in dollars Let N be the number of copies of the book produced For the first printing the company can produce up to 200 copies of the book Suppose that C 20N 500 gives C as a function of N during the first printing Identify the correct description of the values in both the domain and range of the function Then for each choose the most appropriate set of values Domain Range Description of Values Onumber of copies produced O cost of publishing book in dollars Onumber of copies produced O cost of publishing book in dollars Set of Values Choose one Choose one

Under 41 Y oung 41 to 55 M iddle aged Over 55 S enior Total K An exercise video company surveyed its customers to determine whether they prefer to purchase videos using an access code to download them from a website purchase them on DVDs or access them via a podcast The results are shown in the table Use the table to find the cardinal number of the set A YUS Access Code A Podcast P 12 32 13 57 22 46 31 99 The cardinal number of the set A Y US is DVD D 8 6 7 21 Simplify your answer Total 42 84 Points 0 of 1 51 177 Save

K In the set of the ten top grossing movies of all time define the sets shown below the set of movies that earned more than 900 million the set of movies that won a movie award B the set of movies that were made before 1970 Describe the set En B in words and then find the set E A Define the set En B in words Choose the correct answer below A The set of movies that earned more than 900 million and were made before 1970 O B The set of movies that earned more than 900 million and were made after 1970 OC The set of movies that earned less than 900 million or were made after 1970 D The set of movies that earned more than 900 million or were made before 1970 Identify the elements of the set En B Type the letter s of the movie s that are in the specified set For example an answer could be En B a b m EnB Use a comma to separate answers as needed Data table 11111 Movie Movie a Movie b Movie c Movie d Movie e Movie f Year 1958 1942 1965 1979 1983 1934 Inflation Adjusted Gross millions 1 326 1 219 985 950 909 883 990 Won Movie Awar Yes Yes Yes Yes Yes No Yes

The numbers in the regions of the given Venn diagram indicate the number of elements in each region Use the diagram to solve for the indicated set n A B 5 A6 10 n A B Simplify your answer

In the universal set U a b c h define subsets of cars with the characteristics shown to the right Describe the following set in words and then find the set WOG Click on the icon to view the table of new car features Define the set Wn G in words Choose the correct answer below 00000 A The set of cars that have 3 or more years warranty or do not have a good safety rating B The set of cars that have 3 or more years warranty and do not have a good safety rating C The set of cars that have 3 or more years warranty and have a good safety rating OD The set of cars that have 3 or more years warranty or have a good safety rating Identify the elements of the set Wn G Select all that apply A e C h E f G a I I Wn G is the empty set B C D d F g H b P price is above 20 000 C is compact G has a good safety rating A has antitheft package W warranty is at least three years

K Let U 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 A 3 7 8 11 12 13 14 15 16 B 1 3 4 5 7 9 12 13 15 and C 1 2 6 7 10 11 12 13 16 Find C B n C A Select the correct choice below and if necessary fill in the answer box to complete your choice OA C B n C A Use a comma to separate answers as needed X OB C B n C A 0

K Determine whether the following pair of sets is equivalent Justify your answer 2 4 6 and a e i Are the sets equivalent OA Yes both sets are subsets of larger sets OB Yes both sets have the same number of elements OC No neither set is a subset of the other OD No the two sets do not have any of the same elements

K Determine whether the following pair of sets is equal and 0 Are the two sets equal or not equal O Not equal O Equal

K Determine whether the set is well defined 1 9 17 25 33 41 Choose the correct answer below OA The set is well defined because the set of numbers follows a specific pattern which determines whether or not an element is a member of the se OB The set is well defined because there is a finite number of elements in this set OC The set is not well defined because there is no pattern which determines whether or not an element is a member of the set OD The set is not well defined because there are an infinite number of elements in this set

K Draw a bag diagram to illustrate the following set and find its cardinal number The cardinal number is

Choose the correct answer below OA January June July OB June July OC January February March April May June July August September October November December OD January June OE

1 point Determine whether the following statements are true or false 1 32 R such that Vy R zy 1 2 V Q Z such that n Z 3 Vr y R ne Z such that na y 4 V R Jy R such that ay 1 5 VxZ By R such that y 6 R such that Vy ER y 0

2 members of a gymnastics team are randomly chosen to compete in an invitational If there are 9 members on the team how many ways could be chosen Your answer

K The owners of the Phoenix Flames football team own different amounts of stock in the franchise so when they vote on an issue they have different amounts of voting power Assume that Alvarez s and Cianci s votes each will count once Belardo s will be counted three times Devlin s five times and Espinoza s six times In order for a motion to be passed the vote must be a total voting weight of at least eight How many different subsets of this group of owners have a voting weight of at least eight Type a whole number n

K Let A 3 4 5 6 7 9 10 11 a How many subsets does A have b How many proper subsets does A have a A has 256 subsets Type a whole number b A has proper subsets Type a whole number

A tree diagram that shows all subsets of set a b c is shown below Think of the top branch as branch 1 the next branch as branch 2 etc Complete parts a and b Choose Choose Choose element a element b element c Yes Yes No No No Yes No Yes No Yes No a Which branch corresponds to the subset c a branch

Find n A for the following set A x x is a vowel in the English alphabet n A 0

Directions For each of the questions in this section show all work to get full marks 1 2 points The terminal arm of an angle 8 in standard position passes through the point A 4 5 a Determine the primary trigonometric ratios to three decimal places sine H Find 3 to the nearest tenth of a degree cos tan

Suppose that for a certain mathematics class the scores are normally distributed with a mean of 75 and a standard deviation of 9 The teacher wishes to give A s to the top 5 of the students and F s to the bottom 5 The next 15 in either direction will be given B s and D s with the other students receiving C s What is the cumulative distribution Grade A BCDF Percent 5 15 15 5 X Cumulative

Which sets of ordered pairs represent linear relations Explain your answers a 1 5 5 5 9 5 13 5 b 1 2 1 4 1 6 1 8 c 2 3 1 2 2 1 4 3

1 point Consider the relations R R R3 R R5 on A R 1 2 2 1 R 2 2 2 3 2 4 3 2 3 3 3 4 R3 1 1 1 2 2 1 2 2 3 3 4 4 R 1 2 2 3 3 4 R 1 1 2 2 3 3 4 4 Determine which of the following statements are true Select all that apply DA R is not symmetric OB R is reflexive OC R is symmetric DD R is transitive DE R is reflexive OF R is transitive G R is not reflexive OH R is reflexive DI R is transitive 3 4 defined by J R3 is not transitive OK R is symmetric

sed to help solve many real world problems For example we can use graph colorings to help us solve situations like the one described below There are 8 people enrolled in the Extended Learning classes as part of a summer study abroad program They are taking the classes as shown in the table Mica Psychology Game Design Beatrix Psychology Literature Jamie Sociology Literature Psychology Game Design Hans Farah Callie Ignacio Landry Ethics Sociology Psychology Business Literature Journalism The host university needs to schedule final exams for these students and would like to use the minimum number of time slots required We can use graph theory to help us analyze this situation D Business Psychology Game Design Sociology Literature Ethics We begin by making a graph using the data in the table Draw the following graph on a piece of paper In our graph each vertex represents one of the classes Two vertices are connected if there is a student taking both of those classes Note that if a student is taking both of those classes then those final exams cannot occur at the same time E C F B G Use the graph you drew to determine what is the minimum number of final exam times slots needed so that the people can take all of their final exams Hint Would a vertex coloring or an edge coloring be more useful here Psychology Sociology Ethics In the following table indicate in which final exam time slot each class could be placed i e 1 2 etc

Use the formula in this example to determine the sample size n The estimated prevalence is 19 and the desired confidence level is 93 with a margin of error of 5 Identify the following values Determine the sample size Round your answer to the nearest integer n

Let A B and C be subsets of a universe U Which of the following is a minset generated by A B and C Select all that apply A ANBOcc DB ANC DC A n AB nCo OD A0 B C DE U AUBUC OE ANB UC

on 9 of 13 Macmillan Learning Find one solution coming from the interval 0 z of the equation 4 cos x 1 4 sin x Suggestion Think about the double angle formula for the cosine Express numbers in exact form Use symbolic notation and fractions where needed x Provide an approximated solution correct to two decimal places Use decimal notation Give your answer to two decimal places If the answer is given in degrees include the degree symbol

Write the equation of the line in slope intercept form y mx b 8 7 6 5 Z 17 www myopenmath com assess2 7cd 1915768 S 8 7 6 5 4 w A 3 2 1 2 3 4 5 67 8 12 on 4 6 78

Multiple Choice Identify the choice that best completes the statement or answers the question 19 Which is the best material to use for special protective clothing Polyester C 100 wool 100 cotton d leather 20 The job of the Flux on the stick electrode is to a Form a slag layer over the weld b Change the characteristic of the arc C Provide a directional support for the molten metal a b 21 There are a few techniques to starting a weld which ones are correct a Tapping C Scratching b Igniting d High Frequency 22 It s important to keep which variables consistent during the welding process Voltage Travel Speed Stick out a b Arc Length a b d e 23 A Defect Discontinuity that consists of air pockets a Lack of Fusion b Excessive Reinforcement 25 Excessive Spatter is cause by too high of amperage too long of arc length a b Slag Inclusion Shield the weld pool All of the above C d 24 A Defect Discontinuity that consists of a non metal piece lodged inside the weld a Porosity c Incomplete Fusion b d a 5 mins b 8 mins C d Porosity C d in the weld sle Slag Inclusion 26 Welding Electrodes with the third digit of 1 ie 7018 means They can only be welded 1 way They are limited to Flat and horizontal C d Incomplete Joint Penetration C d Arc Blow All of the Above 27 If a machine had a duty cycle of 50 125 amps how many minutes could it run 125 amps in a 10 m amps hout mon in cycle Can only be welded flat Can be welded in all positions 6 mins 25 seconds 10 mins

1 2 pts Use numbers from the list 6 7 8 9 10 and or 11 to fill in EIGHT equal sections in a spinner so that the probabilities below will all be true for your spinner you can use the same number in more than one section if appropriate You may need to review MATH 210 concepts The probability of landing on a multiple of 3 is 1 4 The probability of landing on a number that has EXACTLY 2 DIFFERENT prime factors is also 1 4 The probability of landing on an even number is 1 2 The probability of landing on a prime number is 3 8

Assume that in a men s basketball league the distribution of heights has a mean of 6 feet 8 inches and a standard deviation of 5 inches If there are 336 players in the league how many players should be over 7 feet tall Click the icon to view the area under the standard normal curve table Of the 336 players approximately are over 7 feet tall Round to the nearest whole number as needed

Imagine that for those who meditate daily the number of minutes in meditation has mean 32 and standard deviation 7 In a group of 100 such persons how many are expected to meditate more than 36 minutes per day Click the icon to view the table of z scores Of the 100 persons approximately will meditate more than 36 minutes per day Round to the nearest whole number as needed

K The following table lists the number of years of education past high school and the annual income of six people Determine the linear correlation coefficient for the data and also determine whether we can be 95 or 99 confident that there is significant linear correlation between the two variables Years of Education Past High School Annual Income in thousands of 2 30 3 29 4 35 4 32 5 40 Click the icon to view the table of critical values for the linear correlation coefficient 6 C 39 The correlation coefficient between the two variables is r Round to four decimal places as needed Table of critical values a 05 950 878 6 811 7 754 707 666 632 602 576 553 532 514 16 497 17 482 18 468 456 n 4 5 Toolery STONES 8 9 10 11 12 13 14 15 19 01 999 959 917 875 834 798 765 735 708 684 661 641 623 606 590 575 504 X