Sets and Relations Questions and Answers

Let B 4 9 Compute the following sets a B 16 81 b R 61 700

Suppose that subsets of the universe U 1 2 3 4 5 6 7 8 9 10 are encoded by 0 1 bit strings where a 1 in the ith position indicates membership of the ith th element of U 1 Which bit string encodes the subset 2 4 6 8 10 2 To which subset of U does the string 1000000001 correspond 3 To which subset of U does the string 0100111010 correspond 4 Which bit string encodes the subset

Recall the following fact given in class Fact Let S be a finite set with S n Then P S 22 Let S 1 2 3 4 5 6 7 8 9 a How many subsets does S have in total b How many subsets A of S satisfy the property that 2 3 4 5 6 7 8 9 A G Cak Hint It s easy to list all such subsets

Let A 0 3 6 and B 6 5 4 3 6 7 a Compute the power set of A List the elements of the power set separated by commas Answer P A b Compute A x B

Let A and B be subsets of a universe U On each line put a checkmark if and only if the statement is true OA If U is infinite and Ac is finite then A is infinite OB If A is infinite and U is infinite then A is finite OC If A is infinite and B is finite then AUB is infinite OD If A is finite and B is finite then AUB is finite E If A is infinite then A B is infinite E If A is infinite and B is infinite then An B is infinite

Let A 2 5 11 and B 10 22 55 Give the elements of the following set S a b E A x B b is a multiple of a List the elements separated by commas Answer S B

Let A B and C be sets On each line put a checkmark if and only if the statement is true DA A n Bcncc 0 OB An B x C A x B n B x C OC A B n B C n C A 0 OD A B C A C B C OE Ax BUC A x B U A x C OF A C n C B 0

Let A and B be sets On each line put a checkmark if and only if the statement is true OA A B An Bc OB P A x B P A P B OC A x B A x Be OD B B A An B OE P A P A DE AB nA A

4 attempts remaining Use the same instructions as the previous problem Click this link to view the Venn diagram a AUB C Shaded regions b A C en B Shaded regions c ANB UCC Shaded regions Submit answer A 1 4 2 5 7 C 6 3 B E

Consider the following sets contained in the universe U 1 2 3 4 5 6 7 8 A 1 3 4 6 B 3 4 8 Compute the following sets a AUB b An B c AUB d An Be e A B 9

Prob 1 True or false a 5 5 6 b 5 5 6 c 5 5 6 d 0 0 e For every set A 0 A Prob 2 Give an example if there is one of sets A B C such that AB BCH ACC If it is not possible write Not possible Although Venn diagra help visualize the answer you must not rely on these to prove that your exam works Prob 3 Write all the elements of the power set P A for A 0 Prob 4 Let A B be sets Prove that if zB and ACB then r A

Consider the following set A 7 0 8 1 5 e 24 a Determine the largest subset of A consistsing entirely of natural numbers b Determine the largest subset of A consistsing entirely of integers c Determine the largest subset of A consistsing entirely of rational numbers d Determine the largest subset of A consistsing entirely of real numbers

Consider the following sets a Compute the set S A 9 4 8 S 5z 8 ze A T x 5x A b Compute the set T Hint Be sure to read this set correctly see the Edfinity demo

A park ranger measures the height of pine trees in meters and counts the number of unbroken pine cones under the tree after a storm He assumes that height is the explanatory variable His data expressed as ordered pairs is 20 6 10 7 30 4 30 5 and 10 8 What is the correlation coefficient for this data Show all formulas used and all work 14

If n A 4 n B 6 and n C 10 what is the greatest and least number of elements in each of the following a AUBUC b An Bnc a The greatest number of elements is A UBUC is The least number of elements in AUBUC is b The greatest number of elements in An B n C is The least number of elements is An Bn Cis

Describe Dr No as completely as possible Choose the correct answer below O A Dr No is a male spy who is poor and not tall OB Dr No is a poor tall female spy OC Dr No is a male spy who is not poor and not tall OD Dr No is a poor tall male spy Poor Tall Wor Dr

In a fraternity with 34 members 18 take mathematics 5 take both mathematics and literature and 8 take neithe mathematics nor literature How many take literature but not mathematics members take literature but not mathematics

Fill in the Venn diagram with the appropriate numbers based on the following information n A 26 n B 39 n C 23 n AB 13 n B n C 15 n An C 9 n An BnC 5 n U 66 A Venn diagram is a graphical representation of sets Remember that n A is the number of elements in set A Region I contains Region II contains Region III contains containe elements elements elements elements I A II VI VII V IV VIII CI B

2 If the function f x is strictly concave then f x 1 1 XB XA 1 2 XB Where XA and XB are two particular values of x and 0 1 1 A certain consumer s utility function is u x 3ln x Let x 100 x 500 and 0 6 a 25 pts Calculate the following quantities u x 1 x and u x 1 U XB b 25 pts Based on your calculations for part a does this utility function appear to be strictly convex or strictly concave on the interval 100 x 500 Briefly explain X c 25 pts Now interpret the weight as a probability and interpret the x values 100 and 500 as possible dollar payoffs associated with a gamble Here is a simple probability distribution p x u x 3ln x 100 0 6 500 0 4 Again using your calculations from part b does the consumer appear to be a risk averter or a

DS 301 F23 Week 2 In Class Assignment Show detailed calculations calculating the Interquartile Range for the following data 12 32 45 37 50 37 21 27 18 32

Day Frequency Relative Frequency Mon 1504 Tue 1880 Wed 2402 Thur 2566 Fri 3576 Give the relative frequencies for each day Show your deta calculations Use at least four digits to the right of the deci

21 Elan makes time every day at the end of basketball practice to work on his free throws During one week he makes 11 15 19 23 and 27 throws Assuming this sequence continues find the recursive and explicit rules

Use a Venn diagram to answer the question A survey of 118 college students was done to find out what elective courses they were taking Let A the set of those taking art B th set of those taking basket weaving and C the set of those taking canoeing The study revealed the following information n A 45 n B 55 n C 40 n An B 12 n An C 15 n B n C 23 n An BnC 2 How many students were not taking any of these electives OA 36 B 28 C 10 D 26

Let U q r s t u v w x y z be the universal set Let A q s u w y B q s y z and C v w x y z List the members of the indicated set An B OA q s t u v w x y B r s t u v w x z C u w D t v x

If S is a subset of universe U find each of the following a SUS b c Sns d ns a The simplest expression for SUS is b The simplest expression for U is c The simplest expression for SnS is d The simplest expression for ns is

Find the cardinal number of each of the following sets Assume the pattern continues in each part a 19 20 21 97 b 4 6 8 10 1004 a The cardinal number of 19 20 21 22 97 is b The cardinal number of 4 6 8 10 1004 is c The cardinal number of x 1x 1 2 3 63 is d The cardinal number of x x x 6 and XEN is c x x 1 2 3 63 d x x x 6 and XEN

0 7 Round each number to the nearest whole number 1 4 3 9 2 2 8 1

Answer the following Show all pertinent solutions Let A 1 3 5 B 3 5 6 and C 1 3 7 a Verify that An BuC An B u An C b Find Ax B CA B

3 Brent is buying a new laptop for school and can select none some or all of the following choices a peripherals a laser mouse a DVD burner a Web cam or jump drive How many different selections c peripherals are possible for his laptop

Republicans widespread lack of trust in institutions like the news media which sponsors a great dea of polling led some people to not want to participate in polls This indicates a problem of a sampling error instead of reaching out to the general population the polls only reached out Democratic leaning voters and didn t recruit Republican voters b coverage error not using the right communication method to reach to all targeted population e g landline telephone are more likely to reach older people and or those who stay at home for longer time during a day c measurement error not measuring what researcher thought they were measuring i e instead of people s voting preference they were in fact measuring if people are going to vote by mail or in person d non response error not all potential voters contacted were willing to respond to the survey

1 500 people are surveyed and asked to check the boxes that apply to them I am confident in the economy I have health insurance 321 said they were confident about the economy 403 said they had health insurance and 63 checked neither box a 3 pts Draw an accurate Venn diagram that represents the situation consisting of cardinalities Grade breakdown 5 each for correct answer correct work and labeling for calculated regions Work 3 pts Replace these words with a cropped picture of your work Venn diagram for question 1 only b 1 pt How many people had health insurance and were not confident in the economy Answer 0 5 pt Reasoning Explanation 0 5 pt c 1 pt How many people have health insurance or are confident in the economy

Towers may sirothni bas E S 101 10le 14Let A be the set of all letters in the alphabet V a e i o u and N xx E N 1 x 5 True or False a VCA b 5 EN I ei qam ond no slepe srit 11 martion of siloqots most arboniteti qsms no In Smarito of alloqotisM mon ti ai tal worl ront Nave 101 slim c V N d EN identity Property 1 Distributive Property of Multiplication over Addition e A is a finite set antot teswol ni noiosats es edededeaza slink f Y and N are disjoint sets

Use f x 3 2x g x x 7 and h x x 5x to find each function below Be sure to state any domain restrictions wherever necessary 34 8 f x 35 h f x 36 4

Question Which of the following is the set M for all the letters that make up the word MATHEMATICS Select the correct answer below M M T H C S M M A T H E I C S M M A T H E M A T I C S M A E I FEEDBACK MORE INSTRUCTION SUB

Construct a Venn diagram illustrating the sets below U 1 2 3 4 5 6 7 8 9 W 2 4 6 9 Y 1 3 4 5 9 Z 1 4 6 8 1 2 3 5 7 9 4 6 8 U W Z Y

Sets A B and Care subsets of the universal set U These sets are defined as follows U 1 2 3 4 5 6 7 8 9 A 1 2 4 7 B 2 3 7 8 C 4 6 7 8 9 Find AUB n C Write your answer in roster form or as AUB D C

The table lists the eight human blood types It also shows how blood types determine who a person can donate blood to and receive blood from Blood type A B AB AB A B 0 Can donate to A AB B AB AB AB AB A A AB AB B B AB AB A B AB 0 All blood types Can receive from A A 0 0 B B 0 0 All blood types A B AB 0 A O B 0 0 0 0 Let U be the set of all eight human blood types a X b y Y U A B AB AB A B 0 0 Let X be the set of blood types that type 0 can donate blood to Let Y be the set of blood types that type A cannot donate blood to Find the sets below Write each answer in roster form or as 0 A AB 0 X 0 0 B A 0 AB B

Which data set has the same standard deviation as the data set 1 1 3 5 837 O 9 8 9 8 9 O 2 2 4 6 9 O 1 2 6 6 9 O 1 1 1 2 2

1 Determine if T x y x y x y is invertable If so find its inverse

HATA MARSTE 1 11 Find the eigenvaluse and eigenvectors for 1 1 ALLGAT NOT 1 1

Consider the sets A distinct letters in the word keep B 13 C k e p D 2 1 E three F 3 a What is the cardinality of each set A IBI C D E IFI b Which of the sets are equivalent O A CD E F A C DE F 4 O AC B D E F OAB CD E F A C B D E F c Which of the given sets are equal A C D E F A C D E F C E F A C D E F A C B D E F

Draw a Venn diagram for the relationship An B U An C U A A WebAssign Plot C B B U U A A B B

Researchers collected data to examine the relationship between air pollutants and preterm births in Southern California During the study air pollution levels were measured by air quality monitoring stations Suppose the length of gestation data were collected on 145 106 births between the years 1989 and 1993 and air pollution exposure during gestation was calculated for each birth Comment on whether or not the findings of the study can be used to establish causal relationships Since this study is experimental the findings cannot be used to infer causal relationships O Since this study is experimental the findings can be used to infer causal relationships Since this study is observational the results cannot be used to infer causal relationships O Since this study is observational the findings can be used to infer causal relationships None of the above

A research survey asked 2 373 randomly sampled household owners if they preferred solar energy wind energy neither or both 39 of respondents claimed they prefer solar energy while 26 said wind energy 13 responded that they like both solar and wind energy What percent of household owners prefer neither solar nor wind energy 0 48 O 52 0 78 0 22 None of the above

Which of the following statements is true regarding class imbalance A label with class imbalance will always be challenging to model An accuracy of 99 can be bad when there is high class imbalance O Upsampling is always better than downsampling Class imbalance is a pretty rare problem to worry about

swer Are the sets equal 28 30 32 34 36 30 32 34 36 No

2 3 Use the inverse of A 3 125 60 80 30 45 19 26 3 to decode the following 85 120 6 8 10 15 84 117 42 56 90 4

Find the standard deviation for the group of data items 15 11 15 11 15 11 15 11 The standard deviation is Round to two decimal places as needed

9 In a recent survey 180 BCC students were asked what they did during a lockdown drill The results were 80 screamed 92 ran 65 called someone 47 screamed and ran 20 screamed and called someone 25 ran and called someone and 17 did all three 10 pts a Draw a Venn Diagram illustrating the survey u 180

3 problem 3 2 6 b c e Find dfa s that accept the following languages a L ab a ab a aa b L abab aaa b c L aa abb