(b) Three sets are defined as follows:M ={natural numbers < 20}P = {prime numbers < 20}Q = {odd numbers < 20}%3D(i)List the members of M n P(ii)Find the members of P which are not in set Q(iii)Find the members of Q which are not in set P(c) Create a set comprehension for the set F ={1,2,4,8,16} (a) L is a language with L = {r°101°r°10}. Which of the following strings arecontained within L?(i)101011010(ii) 11101110(iii) 0101010(iv)10110(v)1010101010

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Answered: Three sets are defined as follows: M =…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section9.1: Counting

Problem 4E: True or False? In counting combinations, order matters. In counting permutations, order matters. For...

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True or False? In counting combinations, order matters. In counting permutations, order matters. For a set of n distinct object, the number of different combinations of these object is more than the number of different permutations. If we have a set with five distinct objects, then the number of different ways of choosing two members of this set is the same as the number of ways of choosing three members.
Lost on the last three subplots
A set of blocks contains blocks of heights 1, 2, and 4 centimeters. Imagine constructing towers by piling blocks of different heights directly on top of one another. (A tower of height 6 cm could be obtained using six 1 cm blocks, three 2 cm blocks, one 2 cm block with one 4 cm block on top, one 4 cm block with one 2 cm block on top, and so forth.) Let tn be the number of ways to construct a tower of height n cm using blocks from the set. (Assume an unlimited supply of blocks of each size.) Find a recurrence relation for t1, t2, t3, . For each integer, n ≥ 5,
Consider the single object allocation problem discussed in the class. A single object needs to be allocated to one of n agents. Each agent has a value , that is, the utility he derives from the object, if given for free. The game is as follows: ? Each player/agent simultaneously announces a non-negative number - call it his bid. Denote the bid by player i as bi ≥ 0. Highest bidder wins the object - in case of a tie, the bidder with the lowest index wins (for instance, if agents 2, 3, 5 have the highest bid, then 2 wins the object). The winner gets the object for free, i.e., does not pay anything. All other agents ( i.e., those who don’t get the object) receive a payment equal to the highest bid amount. A) Formulate the game in Normal Form. B) Verify whether the game has a weak dominant strategy equilibrium. Explain why, or why not .
2. The physicist Frank Benford noticed in the 1930s that, for many sets of numbers in the real world, the leading digit* of the number is more likely to be a small number than a larger one (i.e., 1’s and 2’s are more common than 8’s and 9’s). In fact, many wide-ranging number sets obey “Benford’s Law,” which says that 1’s are about 30.1% of the leading digits, 2’s are 17.6%, 3’s are 12.5%, 4’s are 9.7%, 5’s are 7.9%, 6’s are 6.7%, 7’s are 5.8%, 8’s are 5.1%, and 9’s are 4.6%. Benford’s Law has been used to identify accounting fraud and made-up scientific data. *leading digit is the first significant digit; e.g., “1” in the number 132, “2” in the number .0026.S uppose I suspect my research collaborator of faking a dataset that represents the price that people say is the average amount they pay each month in health care deductibles and copayments, rounded to the nearest dollar.10 50 15 11 412 80 48 13 4250 10 68 41 790 15 139 147 1433 61 145 7 406 99 50 27 7513 40 3 21 1475 203 148 27…
(The "harem problem") Let B be a set of boys, and suppose that each boy in B wishes to marry more than one of his girl friends. Find a neccessary and sufficient condition for the harem problem to have a solution.(Hint: replace each boy by several identical copies of himself, and then use Hall's theorem.)
Topic: Venn Diagrams and Algebra of Sets Solve the following problem. In a group of 100 freshman students, 36 are enrolled in Algebra, 29 in Trigonometry, and 32 in English. Of these, 11 are taking both Algebra and Trigonometry, 9 both Algebra and English, 12 both Trigonometry and English, and 6 all the three subjects. How many are enrolled in:(a) At least one of the three subjects(b) Neither of the three subjects?
On-Time Performance by Airlines According to the Bureau of Transportation statistics, on-time performance by the airlines is described as follows: Action % of time On time 70.8 National Aviation System delay 8.2 Aircraft arriving late 9.0 Other (because of weather andother conditions) 12.0 Records of 200 flights for a major airline company showed that 148 planes were on time;24 were delayed because of weather, 8 because of a National Aviation System delay, and the rest because of arriving late. At =α0.05, do these results differ from the government's statistics? Part: 0 / 5 0 of 5 Parts Complete Part 1 of 5 Identify the claim with the correct hypothesis. H0: On-time performance by airlines is distributed as follows: 70. 8% on-time,8.2% National Aviation System delay, 9.0% aircraft arriving late, and 12.0% other. ▼(Choose one) H1 : The distribution is not the same as stated in the null hypothesis. ▼(Choose…

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Three sets are defined as follows: M = {natural numbers < < 20} P = {prime numbers < 20} Q = {odd numbers < 20} (i) List the members of M n P (ii) Find the members of P which are not in set Q (ii) Find the members of Q which are not in set P