Sets and Relations Questions and Answers

The impulse response of the discrete causal system is y n 2y n 1 3x n 1 is 01 h n 3 2 2u n 2 O 2 h n 32 22n 1u n 1 O 3 None of the answers 4 h n 3 2 lu n 1 h n 2 u n 1 05

A truth value assignment that makes all the premises of an argument true and its conclusion false is called a 2 point

Question 9 N Consider the following statements int p int i int k i 37 k i p i After these statements which of the following will change the value of i to 75 Ok 75 O k 75 O p 75 O p 75 OTwo or more of the answers will change i to 75

rove that the relation R defined on the set X Z by mRn 3m 2 n is divisible by 5 is an equivalence relation Determine its equivalence classes 0 R 7 R 1 many different equivalence classes does this relation h

pA pv q q A p q v q pv T by negation law p pv q q pv qv q by associative law FV p q q by negation law pvF by negation law pv q vq by De Morgan s law

Required information NOTE This is a multi part question Once an answer is submitted you will be una Fill the given truth table Fill the truth table for Click to select p You must provide an Click to select noving to the next part PAP Click to select P p

Complete the truth table given below to verify the first De Morgan law p Aq p V q p q 7P79 TT Click to select F p q Click to select T PV q FF Click to select T TA FIT FT Click to select F Click to select TF Click to select TIT T T V

P T T p p q Click to select Click to select Click to select Click to select Click to select Click to select Click to select The conditional statement is p p q is a Click to select Click to select F Required information NOTE This is a multi part question Once an answer is submitted you will be L Fill the provided truth tables and check whether the given conditional stateme contingency F q T F T p F F T T F p q Click to select contigency tautology contradiction

Suppose an x distribution has mean 2 Consider two corresponding x distributions the first based on samples of size n 45 and the second based on samples of size n 81 LAUSE SALT a What is the value of the mean of each of the two x distributions for n 49 distribution for n 81 distribution b For which x distribution is P x 2 50 smaller Explain your answer The distribution with n 49 because the standard deviation will be larger The distribution with n 81 because the standard deviation will be smaller The distribution with n 49 because the standard deviation will be smaller The distribution with n 81 because the standard deviation will be larger c For which x distribution is P 1 50 x 2 50 greater Explain your answer The distribution with n 81 because the standard deviation will be larger The distribution with n 49 because the standard deviation will be smaller The distribution with n 81 because the standard deviation will be smaller The distribution with n 49 because the standard deviation will be larger

The graph of y f x is shown below 1 b Is f x continuous at x 1 OYes No Answer each of the following questions about f x You have one submission for each question a Does lim f x exist x 1 OYes No c Is f x differentiable at x 1 Yes No d Does lim f x exist X 2 OYes No The graph of a parabola that opens up with a hollow point on the graph when x 2 e Is f x continuous at x 2 OYes No f Is f x differentiable at x 2 2

Which of the following are possible examples of sampling distributions Select all that apply average male height based on samples of size 30 average SAT score of a sample of high school students all mean trout lengths in a sampled lake mean trout lengths based on samples of size 5 heights of college students at a sampled university

f x 2x g x x x 3 Find f g 1 5 11 6

Solve for x Enter your answers as a comma separated list 2 x x 31 9 0

Consider the following linear system 2x1 x1kx22x3 k 1 x3 1 k 3kx2 k 4 3 3 k

9 7 4 pts Write a formula for the rational function graph 8 6 5 3 2 1 17 10 8 9 3 2 0 2 3 4 5 6 7 8 3x 1x 6

For all sets A B and C if AC B then AnCc is O a Anc CBC O b ANCC BNC OC ANC BNC O d AnCBUC

What is the age distribution of promotion sensitive shoppers A supermarket super shopper is defined as a shopper for whom at least 70 of the items purchased were on sale or purchased with a coupon Age range years 18 28 Midpoint x Percent of super shoppers 5 For the 62 and over group use the midpoint 67 years a Using the age midpoints x and the percentage of super shoppers do we have a valid probability distribution Explain Step 1 23 c Compute the expected age of a super shopper 29 39 40 50 51 61 34 b Use a histogram to graph the probability distribution of part a 45 42 0 05 0 42 0 18 0 12 1 d Compute the standard deviation o for ages of super shoppers 18 In order to have a valid probability distribution 2 conditions must be met 56 12 62 and over 67 a Using the age midpoints x and the percentage of super shoppers do we have a valid probability distribution Explain 23 1 The probability distribution has a probability assigned to each distinct value of the random variable 2 The sum of all the assigned probabilities must be 1 We can see from the table that each distinct value of the random variable has been assigned a probability Use these probabilities to check if the sum of all the assigned probabilities is equal to 1 P x P 23 P 34 P 45 P 56 P 67

5 Let P be the polygon with vertices 1 0 2 0 4 1 4 2 3 4 2 4 0 3 0 2 taken in that order Find all isometries of P What group do they form 6 Let Q be the polygon with vertices 1 0 2 0 4 2 4 3 3 4 2 4 0 2 0 1 taken in that order Find all isometries of Q What group do they form 7 Which of the groups introduced above in Problems 3 6 are pairwise iso morphic and which are not

Sammy Aww thank you so much That means a lot to me and yes I got all my grades except for one of my classes I have three A and one A I miss you so much Ms Christmas Yes I miss you as well Even if I don t see you during your break I will definitely come and see you at Harvard

Let A and B denote two events defined on the same sample space If P A 0 7 P B 0 3 then If the events A and B are mutually exclusive disjoint the value of P AU B equals to O a 0 68 O b 1 0 O C O d 0 7 O e 0 79 P Flag question 0 21

Let A and B be two events defined on the same sample space such that p AB 0 5 P ANB 0 2 and p AB 0 1 Then p AUB O a 0 1 O b 0 0 O C NOTA O d 0 44 O e 0 9

Not yet Let A and B be events defined on the same sample space such that p AB 0 5 P ANB 0 2 and P AB 0 1 Then P A O a 0 3 O b None is correc O c 0 7 O d 0 2 Oe 0 4

7 y f x 1 f x

Find ATA and AAT A 1 1 5 0 2 a ATA 100 b AAT 000 4

Use the Venn diagram to write the elements of B Enter your answer as a set using the listing method 1 A kg d E h n B i j a b U

Use the Venn diagram to write the elements of BC Enter your answer as a set using the listing method a A mf h C n DO g j B k b 1 d U

2 For what values of parameters a b E R the operation x y xy ax by 2 defined for x y E R is commutative and associative 3 For G 1 3 5 9 and xoy defined as the last decimal digit of the number xy 3x 3y 4 i show that o is a well defined operation on G and present its table ii find the neutral element of o iii prove that G o is a group

Let B 2 4 6 8 10 and C 12 13 14 15 16 Write Cn B using the listing method Enter EMPTY or for the empty set COB

Combine the Multiplication Principle and combinations to answer the question The Latarue Company has 6 women and 12 men on its board of directors In how many different ways can a gender equality subcommittee of 6 be formed so that the numbers of men and women are equal ways

Use the Venn diagram to write the elements of A Enter your answer as a set using the listing method k A a 1 b bo P e B C i n E h U

Let U x x is a whole number and 1 x 15 and C 11 12 13 14 15 Write C n U using the listing method Enter EMPTY or for the empty set Cn U

Let B 0 2 4 6 8 10 and C 15 16 17 18 19 Write Cu B using the listing method CUB

Let B 2 4 6 8 10 and C 12 13 14 15 16 Write C n B using the listing method Enter EMPTY or for the empty set Cn B

The value s of a such that the matrix O a R 2 O b None O c 2 O d R 0 O e R 1 Of R 1 1 0 2 1 1 0 1 2 a is nonsingular

Rolls of coiled wire are monitored using a c chart Twenty rolls have been examined and the number of defects per roll has been recorded in the following table Using the set of 20 observations perform run tests on the data What can you conclude about the data Sample Number of Defects Sample Number of Defects 11 1 2 3 1667599 8 9 10 Test First Second 3 2 5 1 2 2422N 1 2 Conclusion Non random 12 13 14 15 16 17 18 19 20 3 4 2 2 SAWN WI 4 52

1 Consider the three sets A the set of all even numbers B 2 4 6 C 2 3 4 6 a is set B a subset of set A b is set A a subset of set C c is set B a proper subset of set C write your answer in sentence form Yes No answer will not earn any credit 2 Consider the sets below Let U 1 2 3 10 A 1 3 5 7 B 1 2 3 4 C 3 4 6 7 9 1 Write the complement of set A use the proper set notation 2 Write the complement of set B use the proper set notation 3 Write AU B in set notation form 4 Write CnA in set notation 5 Write the set C

6 P x 2 x 7 write all the elements in set P 7 Q x 2 x 7 write all the elements in set Q 8 Is set P equivalence to set Q 9 R 1 2 3 4 5 6 and S 2 4 6 is set S a subset of set R 10 From question number 9 is set R a subset of set S 11 Write an example of a null or empty set 12 What is a proper subset and give an example of a proper subset

1 The set A 1 3 5 What is a larger set this might be a subset of 2 Given the set A a b c d List all of the subsets of A 3 From the given set A in number 2 what is the cardinality of set A 4 Given M set of days in the week what is the cardinality of set M 5 If set M set of days in the week and set S set of Snow White s dwarves is set M equivalence with set S why or why not

d Let A and B be subsets of a universal set U Show that A CB if and only if BCA

c Let A B and C be three sets Draw the Venn diagrams for each of these combinations i AnBnC ii A B U A C U B C

a Let A 1 2 3 4 B 3k k Z 1 1 and C n e Zn n Which one of the following statements is True Explain your answer i AnB 0 ii B C 0 iii BnC 0 iv AUC 0

b Let A and B be two sets Show that if ACB then i AUB B ii AnB A

o One of the following function f R R below is a bijection Which one is it Explain your answer i f x x x for all x ER ii f x x x for all x ER iii f x x x for all x ER iv f x x x for all x ER

4 The highest priority for wildfire management officials is to preserve a natural resources b infrastructure c buildings and structures d human life

4 Determine whether each of the following is true or false i 5 EN ii 0 0 iii If A B then AUB nA B ii Compute c b a b C a a a a b a b C 5 The multiplication table above is defined on the set S a b c Is a binary operation on S Explain why or why not i C a C b iii Does S have an identity with respect to If so what is it If not explain why not iv Which elements are invertible For each such element state its inverse v Is commutative in S Why or why not vi Let T be the set of invertible elements in S Determine if T is a group a mc that is not a group a semigroup that is not a monoid or not a semigroup Explain

Consider the function y x 3 a State the transformations b Graph the parent function Graph the transformed functio

The authors of a paper were interested in estimating the mean time that patients who broke a hip had to wait for surgery before and after the opening of a new hospital facility They reported that for a representative sample of 405 patients seen at this hospital before the new facility was opened the mean wait time for surgery was 31 1 hours and the standard deviation of wait times was 27 0 hours For a representative sample of 214 patients seen after the new facility was opened the mean wait time for surgery was 28 7 hours and the standard deviation of wait times was 16 2 hours USE SALT a Construct a 95 confidence interval for the mean wait time in hours of patients seen before the new facility was opened Enter your answer using interval notation Round your numerical values to three decimal places hr Interpret the previously found interval We are 95 confident that the true mean wait time of patients in this sample who were seen before the new facility was opened falls within this interval We can say that 95 of all patient wait times before the new facility was opened fall within this interval There is a 95 chance that the true mean wait time of patients in this sample who were seen before the new facility was opened falls within this interval We are 95 confident that the true mean wait time of patients seen before the new facility was opened falls within this interval There is a 95 chance that the true mean wait time of patients seen before the new facility was opened falls within this interval b Construct a 95 confidence interval for the mean wait time in hours of patients seen after the new facility was opened Enter your answer using interval notation Round your numerical values to three decimal places hr MY NOTES Interpret the previously found interval There is a 95 chance that the true mean wait time of patients in this sample who were seen after the new facility was opened falls within this interval We are 95 confident that the true mean wait time of patients in this sample who were seen after the new facility was opened falls within this interval We can say that 95 of all patient wait times after the new facility was opened fall within this interval We are 95 confident that the true mean wait time of patients seen after the new facility was opened falls within this interval There is a 95 chance that the true mean wait time of patients seen after the new facility was opened falls within this interval

Children with ADHD Do children diagnosed with attention deficit hyperactivity disorder ADHD have smaller brains than children without this condition This question was the topic of a research study Brain scans were completed for a representative sample of 152 children with ADHD and a representative sample of 139 children without ADHD Summary values for total cerebral volume in cubic milliliters are given in the following table USE SALT n ML3 152 Children without ADHD 139 1 104 7 Interpret the interval X S 1 058 5 116 3 111 7 MY NOTES Construct a 95 confidence interval estimate of the difference in mean brain volume in mL3 for children with and without ADHD Use With ADHD Without ADHD Use technology to calculate your critical value Enter your answer using interval notation Round your numerical values to two decimal places PRACTICE ANOTHER We are 95 confident that the true difference in mean brain volume for children with ADHD and the mean brain volume for children without ADHD falls within interval The bounds of the interval suggest the mean brain volume is higher for those without ADHD this

What is the probability that person chosen at random prefers math and econ Math Econ 130 100 90 A 0 889 B 100 0 278 D 0 611 40

3 Prescribed dosage of a certain drug is 11 mg kg that is 11 milligram is admin istered daily for each Kilogram of patient s weight How many 100 mg tablets should be given each day to a patient who weighs 185 pounds 1 lb 0 45 kg 7 pts