Discrete Mathematics And Its Applications 7th Edition
7th Edition
ISBN: 9781259152153
Author: Kenneth H. Rosen
Publisher: MCG CUSTOM
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Chapter 9, Problem 35SE
To determine
To show:
Show that the principle of well-founded induction is valid.
A relation
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The following ordered data list shows the data speeds for cell phones used by a
telephone company at an airport:
A. Calculate the Measures of Central Tendency from the ungrouped data list.
B. Group the data in an appropriate frequency table.
C. Calculate the Measures of Central Tendency using the table in point B.
D. Are there differences in the measurements obtained in A and C? Why (give at
least one justified reason)?
I leave the answers to A and B to resolve the remaining two.
0.8
1.4
1.8
1.9
3.2
3.6
4.5
4.5
4.6
6.2
6.5
7.7
7.9
9.9
10.2
10.3
10.9
11.1
11.1
11.6
11.8
12.0
13.1
13.5
13.7
14.1
14.2
14.7
15.0
15.1
15.5
15.8
16.0
17.5
18.2
20.2
21.1
21.5
22.2
22.4
23.1
24.5
25.7
28.5
34.6
38.5
43.0
55.6
71.3
77.8
A. Measures of Central Tendency
We are to calculate:
Mean, Median, Mode
The data (already ordered) is:
0.8, 1.4, 1.8, 1.9, 3.2, 3.6, 4.5, 4.5, 4.6, 6.2, 6.5, 7.7, 7.9, 9.9, 10.2, 10.3, 10.9,
11.1, 11.1, 11.6,
11.8, 12.0, 13.1, 13.5, 13.7, 14.1, 14.2, 14.7, 15.0, 15.1, 15.5,…
A tournament is a complete directed graph, for each pair of vertices x, y either (x, y) is an arc or
(y, x) is an arc. One can think of this as a round robin tournament, where the vertices represent
teams, each pair plays exactly once, with the direction of the arc indicating which team wins.
(a) Prove that every tournament has a direct Hamiltonian path. That is a labeling of the teams
V1, V2,..., Un so that vi beats Vi+1. That is a labeling so that team 1 beats team 2, team 2
beats team 3, etc.
(b) A digraph is strongly connected if there is a directed path from any vertex to any other
vertex. Equivalently, there is no partition of the teams into groups A, B so that every team
in A beats every team in B. Prove that every strongly connected tournament has a directed
Hamiltonian cycle. Use this to show that for any team there is an ordering as in part (a) for
which the given team is first.
(c) A king in a tournament is a vertex such that there is a direct path of length at most 2 to
any…
Use a graphing utility to find the point of intersection, if any, of the graphs of the functions. Round your result to three decimal places. (Enter NONE in any unused answer blanks.)
y = 100e0.01x
(x, y) =
y = 11,250
×
Chapter 9 Solutions
Discrete Mathematics And Its Applications 7th Edition
Ch. 9.1 - t the ordered pairs in the...Ch. 9.1 - a) List all the ordered pairs in the relation R =...Ch. 9.1 - each of these relations on the set {1, 2, 3, 4},...Ch. 9.1 - ermine whether the relationRon the set of all...Ch. 9.1 - ermine whether the relationRon the set of all Web...Ch. 9.1 - ermine whether the relationRon the set of all real...Ch. 9.1 - ermine whether the relationRon the set of all...Ch. 9.1 - w that the relationR=Oon a nonempty set S is...Ch. 9.1 - Show that the relationR=on the empty setS=is...Ch. 9.1 - e an example of a relation on a set that is a)...
Ch. 9.1 - Which relations in Exercise 3 are irreflexive?Ch. 9.1 - Which relations in Exercise 4 are irreflexive?Ch. 9.1 - Which relations in Exercise 5 are irreflexive?Ch. 9.1 - Which relations in Exercise 6 are irreflexive?Ch. 9.1 - Can a relation on a set be neither reflexive nor...Ch. 9.1 - Use quantifiers to express what it means for a...Ch. 9.1 - Give an example of an irreflexive relation on the...Ch. 9.1 - Which relations in Exercise 3 are asymmetric?Ch. 9.1 - Which relations in Exercise 4 are asymmetric?Ch. 9.1 - Which relations in Exercise 5 are asymmetric?Ch. 9.1 - Which relations in Exercise 6 are asymmetric?Ch. 9.1 - Must an asymmetric relation also be antisymmetric?...Ch. 9.1 - Use quantifiers to express what it means for...Ch. 9.1 - Give an example of an asymmetric relation on the...Ch. 9.1 - many different relations are there from a set...Ch. 9.1 - Rbe the relationR={(a,b)ab}on the set of integers....Ch. 9.1 - Rbe the relationR={(a,b) |adividesb} on the set of...Ch. 9.1 - Let R be the relation on the set of all states in...Ch. 9.1 - pose that the functionffromAtoBis a one-to-one...Ch. 9.1 - R1= {(1, 2), (2, 3), (3, 4)} andR2= {(1, 1), (1,...Ch. 9.1 - Abe the set of students at your school andBthe set...Ch. 9.1 - Rbe the relation {(1, 2), (1, 3), (2, 3), (2,4),...Ch. 9.1 - 33.LetRbe the relation on the set of people...Ch. 9.1 - rcises 34-38 deal with these relations on the set...Ch. 9.1 - rcises 34-38 deal with these relations on the set...Ch. 9.1 - rcises 34-38 deal with these relations on the set...Ch. 9.1 - rcises 34-38 deal with these relations on the set...Ch. 9.1 - rcises 34-38 deal with these relations on the set...Ch. 9.1 - d the relationsS2fori= 1, 2, 3,4, , 6i’here...Ch. 9.1 - Rbe the parent relation on the set of all people...Ch. 9.1 - Rbe the relation on the set of people with...Ch. 9.1 - R1andR2be the divides” and ‘is a multiple of...Ch. 9.1 - R1andR2be the “congruent modulo 3” and the...Ch. 9.1 - List the 16 different relations on the set {0,1}.Ch. 9.1 - How many of the 16 different relations on {0,1}...Ch. 9.1 - ch of the 16 relations on {o, 1}, which you listed...Ch. 9.1 - a) How many relations are there on the set...Ch. 9.1 - S be a set withnelements and letaandbbe distinct...Ch. 9.1 - How many relations are there on a set...Ch. 9.1 - How many transitive relations are there on a set...Ch. 9.1 - d the error in the “proof” of the following...Ch. 9.1 - pose thatRandSare reflexive relations on a setA....Ch. 9.1 - w that the relationRon a setAis symmetric if and...Ch. 9.1 - w that the relationRon a setAis antisymmetric if...Ch. 9.1 - w that the relationRon a setAis reflexive if and...Ch. 9.1 - w that the relationRon a setAis reflexive if and...Ch. 9.1 - Rbe a relation that is reflexive and transitive....Ch. 9.1 - Rbe the relation on the set {1, 2, 3,4 , 5}...Ch. 9.1 - Rbe a reflexive relation on a setA. Show thatRnis...Ch. 9.1 - Prob. 60ECh. 9.1 - Suppose that the relationRis irreflexive....Ch. 9.1 - ive a big-O estimate for the number of integer...Ch. 9.2 - List the triples in the relation {(a, b, c)|a,...Ch. 9.2 - ch 4-tuples are in the relation {(a,b, c, d)| a,...Ch. 9.2 - Prob. 3ECh. 9.2 - uming that no newn-tuples are added, find all the...Ch. 9.2 - Prob. 5ECh. 9.2 - uming that no new n-tuples are added, find a...Ch. 9.2 - Prob. 7ECh. 9.2 - Prob. 8ECh. 9.2 - 5-tuples in a 5-ary relation represent these...Ch. 9.2 - What do you obtain when you apply the selection...Ch. 9.2 - What do you obtain when you apply the selection...Ch. 9.2 - What do you obtain when you apply the selection...Ch. 9.2 - t do you obtain when you apply the selection...Ch. 9.2 - t do you obtain when you apply the...Ch. 9.2 - Prob. 15ECh. 9.2 - Display the table produced by applying the...Ch. 9.2 - play the table produced by applying the...Ch. 9.2 - many components are there in then-tuples in the...Ch. 9.2 - Construct the table obtained by applying the join...Ch. 9.2 - w that ifC1andC2are conditions that elements of...Ch. 9.2 - w that if C1andC2are conditions that elements...Ch. 9.2 - Prob. 22ECh. 9.2 - Prob. 23ECh. 9.2 - w that ifCis a condition that elements of the nary...Ch. 9.2 - w that ifRandSare bothn-ary relations,...Ch. 9.2 - Give an example to show that ifRandSare bothn-ary...Ch. 9.2 - e an example to show that ifRandSare bothn-ary...Ch. 9.2 - a) What are the operations that correspond to the...Ch. 9.2 - Prob. 29ECh. 9.2 - Prob. 30ECh. 9.2 - ermine whether there is a primary key for the...Ch. 9.2 - Show that ann-aryrelation with a primary key can...Ch. 9.2 - Prob. 33ECh. 9.2 - Prob. 34ECh. 9.2 - Prob. 35ECh. 9.2 - Prob. 36ECh. 9.2 - Prob. 37ECh. 9.2 - Prob. 38ECh. 9.2 - Prob. 39ECh. 9.2 - Show that if an item set is frequent in a set of...Ch. 9.2 - Prob. 41ECh. 9.3 - resent each of these relations on {1, 2, 3} with a...Ch. 9.3 - resent each of these relations on {1, 2,3, 4} with...Ch. 9.3 - List the ordered pairs in the relations on {1, 2,...Ch. 9.3 - t the ordered pairs in the relations on {1,2,3,4)...Ch. 9.3 - can the matrix representing a relationRon a setAbe...Ch. 9.3 - can the matrix representing a relationRon a setAbe...Ch. 9.3 - ermine whether the relations represented by the...Ch. 9.3 - Determine whether the relation represented by the...Ch. 9.3 - many nonzero entries does the matrix representing...Ch. 9.3 - many nonzero entries does the matrix representing...Ch. 9.3 - How can the matrixR, the complement of the...Ch. 9.3 - How can the matrix forR1, the inverse of the...Ch. 9.3 - LetRbe the relation represented by the matrix...Ch. 9.3 - R1andR2be relations on a setArepresented by the...Ch. 9.3 - Rbe the relation represented by the matrix...Ch. 9.3 - Rbe a relation on a set A withnelements. If there...Ch. 9.3 - Rbe a relation on a set A withnelements. If there...Ch. 9.3 - Draw the directed graphs representing each of the...Ch. 9.3 - Draw the directed graphs representing each of the...Ch. 9.3 - Draw the directed graph representing each of the...Ch. 9.3 - Draw the directed graph representing each of the...Ch. 9.3 - Draw the directed graph that represents the...Ch. 9.3 - Exercises 23-28 list the ordered pairs in the...Ch. 9.3 - Exercises 23-28 list the ordered pairs in the...Ch. 9.3 - Prob. 25ECh. 9.3 - Prob. 26ECh. 9.3 - Prob. 27ECh. 9.3 - Exercises 23-28 list the ordered pairs in the...Ch. 9.3 - can the directed graph of a relationRon a finite...Ch. 9.3 - How can the directed graph of a relationRon finite...Ch. 9.3 - ermine whether the relations represented by the...Ch. 9.3 - ermine whether the relations represented by the...Ch. 9.3 - LetRbe a relation on a setA, Explain how to use...Ch. 9.3 - Rbe a relation on a set A. Explain how to use the...Ch. 9.3 - w that ifMRis the matrix representing the...Ch. 9.3 - Prob. 36ECh. 9.4 - Rbe the relation on the set {o, 1, 2, 3}...Ch. 9.4 - LetRbe the relation{(a,b)ab}on the set of...Ch. 9.4 - Rbe the relation{(a,b)| adividesb} on the set of...Ch. 9.4 - How can the directed graph representing the...Ch. 9.4 - Exercises 5-7 draw the directed graph of the...Ch. 9.4 - Exercises 5-7 draw the directed graph of the...Ch. 9.4 - Prob. 7ECh. 9.4 - How can the directed graph representing the...Ch. 9.4 - d the directed graphs of the symmetric closures of...Ch. 9.4 - Find the smallest relation containing the relation...Ch. 9.4 - Prob. 11ECh. 9.4 - Suppose that the relationRon the finite setAis...Ch. 9.4 - Prob. 13ECh. 9.4 - Prob. 14ECh. 9.4 - n is it possible to define the ‘irreflexive...Ch. 9.4 - Prob. 16ECh. 9.4 - Prob. 17ECh. 9.4 - Prob. 18ECh. 9.4 - Rbe the relation on the set{1,2,3,4,5} containing...Ch. 9.4 - Rbe the relation that contains the pair (a,b)...Ch. 9.4 - Rbe the relation on the set of all students...Ch. 9.4 - Suppose that the relationRis reflexive. Show...Ch. 9.4 - Suppose that the relationRis symmetric. Show...Ch. 9.4 - pose that the relationRis irreflexive. Is the...Ch. 9.4 - Algorithm 1 to find the transitive closures of...Ch. 9.4 - Algorithm 1 to find the transitive closures of...Ch. 9.4 - Use Warshall’s algorithm to find the transitive...Ch. 9.4 - Warshall’s algorithm to find the transitive...Ch. 9.4 - d the smallest relation containing the relation...Ch. 9.4 - Finish the proof of the case whenabin Lemma 1.Ch. 9.4 - orithms have been devised that use Q(n2,8) bit...Ch. 9.4 - Devise an algorithm using the concept of interior...Ch. 9.4 - Adapt Algorithm 1 to find the reflexive closure of...Ch. 9.4 - pt Warshall’s algorithm to find the reflexive...Ch. 9.4 - Prob. 35ECh. 9.4 - Prob. 36ECh. 9.5 - Which of these relations on {0, 1, 2,3) are...Ch. 9.5 - ch of these relations on the set of all people are...Ch. 9.5 - ch of these relations on the set of all functions...Ch. 9.5 - ine three equivalence relations on the set of...Ch. 9.5 - Define three equivalence relations on the set of...Ch. 9.5 - ine three equivalence relations on the set of...Ch. 9.5 - Show that the relation of logical equivalence on...Ch. 9.5 - Rbe the relation on the set of all sets of real...Ch. 9.5 - pose thatAis a nonempty set, andfis a function...Ch. 9.5 - pose thatAis a nonempty set andRis an equivalence...Ch. 9.5 - w that the relationRconsisting of all pairs (x, y)...Ch. 9.5 - w that the relationRconsisting of all pairs(x,...Ch. 9.5 - w that the relationRconsisting of all pairs (x, y)...Ch. 9.5 - R be the relation consisting of all pairs (x,y)...Ch. 9.5 - Rbe the relation on the set of ordered pairs of...Ch. 9.5 - Let R be the relation on the set of ordered pairs...Ch. 9.5 - (Requires calculus) a) Show that the relationRon...Ch. 9.5 - Prob. 18ECh. 9.5 - Rbe the relation on the set of all URLs (or Web...Ch. 9.5 - Rbe the relation on the set of all people who have...Ch. 9.5 - Prob. 21ECh. 9.5 - Prob. 22ECh. 9.5 - Exercises 21-23 determine whether the relation...Ch. 9.5 - Determine whether the relations represented by...Ch. 9.5 - w that the relationRon the set of all bit stings...Ch. 9.5 - t are the equivalence classes of the equivalence...Ch. 9.5 - t are the equivalence classes of the equivalence...Ch. 9.5 - t are the equivalence classes of the equivalence...Ch. 9.5 - What is the equivalence class of the bit string...Ch. 9.5 - t are the equivalence classes of these bit strings...Ch. 9.5 - What are the equivalence classes of the bit...Ch. 9.5 - What are the equivalence classes of the bit...Ch. 9.5 - t are the equivalence classes of the bit strings...Ch. 9.5 - t are the equivalence classes of the bit strings...Ch. 9.5 - t is the congruence class [n]5(that is, the...Ch. 9.5 - What is the congruence class [4]mwhenmis a) 2? b)...Ch. 9.5 - Give a description of each of the congruence...Ch. 9.5 - t is the equivalence class of each of these...Ch. 9.5 - a) What is the equivalence class of(1,2)with...Ch. 9.5 - a) What is the equivalence class of (1, 2) with...Ch. 9.5 - ch of these collections of subsets are partitions...Ch. 9.5 - ch of these collections of subsets are partitions...Ch. 9.5 - ch of these collections of subsets are partitions...Ch. 9.5 - ch of these collections of subsets are partitions...Ch. 9.5 - Prob. 45ECh. 9.5 - ch of these are partitions of the set of real...Ch. 9.5 - t the ordered pairs in the equivalence relations...Ch. 9.5 - t the ordered pairs in the equivalence relations...Ch. 9.5 - w that the partition formed from congruence...Ch. 9.5 - w that the paron of the set of people living in...Ch. 9.5 - w that the partition of the set of bit strings of...Ch. 9.5 - Exercises 52 and 53,Rnrefers to the family of...Ch. 9.5 - Exercises 52 and 53,Rnrefers to the family of...Ch. 9.5 - pose thatR1andR2are equivalence relations on a...Ch. 9.5 - d the smallest equivalence relation on the set...Ch. 9.5 - pose thatR1andR2are equivalence relations on the...Ch. 9.5 - sider the equivalence relation fromExample...Ch. 9.5 - Each bead on a bracelet with three beads is either...Ch. 9.5 - Let R be the relation on the set of all colorings...Ch. 9.5 - a) LetRbe the relation on the set of functions...Ch. 9.5 - Determine the number of different equivalence...Ch. 9.5 - Determine the number of different equivalence...Ch. 9.5 - Do we necessarily get an equivalence relation when...Ch. 9.5 - Do we necessarily get an equivalence relation when...Ch. 9.5 - pose we useTheorem 2to form a partitionP froman...Ch. 9.5 - .Suppose we useTheorem 2to form an equivalence...Ch. 9.5 - ise an algorithm to find the smallest equivalence...Ch. 9.5 - p(n)denote the number of different equivalence...Ch. 9.5 - Use Exercise 68 to find the number of different...Ch. 9.6 - ch of these relations on {0,1,2,3) are partial...Ch. 9.6 - ch of these relations on {0,1,2,3} are partial...Ch. 9.6 - Prob. 3ECh. 9.6 - Prob. 4ECh. 9.6 - ch of these are posets? a)(Z,=) b)(Z,) c)(Z,)...Ch. 9.6 - Which of these are posets?a) (R, =)b) (R,<) c)...Ch. 9.6 - Determine whether the relations represented by...Ch. 9.6 - Determine whether the relations represented by...Ch. 9.6 - Exercises9-11determine whether the relation with...Ch. 9.6 - Exercises9-11determine whether the relation with...Ch. 9.6 - Exercises 9-11 determine whether the relation with...Ch. 9.6 - Prob. 12ECh. 9.6 - d the duals of these posets. a)({0,1,2},) b)(Z,)...Ch. 9.6 - ch of these pairs of elements are comparable in...Ch. 9.6 - Prob. 15ECh. 9.6 - Let S = {1,2,3,4). With respect to the...Ch. 9.6 - d the lexicographic ordering of thesen-tuples: a)...Ch. 9.6 - d the lexicographic ordering of these strings of...Ch. 9.6 - d the lexicographic ordering of the bit strings...Ch. 9.6 - w the Hasse diagram for the greater than or equal...Ch. 9.6 - w the Hasse Diagram for the less than or equal to...Ch. 9.6 - Prob. 22ECh. 9.6 - Prob. 23ECh. 9.6 - w the Hasse diagram for inclusion on the...Ch. 9.6 - Exercises 25-27 list all ordered pairs in the...Ch. 9.6 - Exercises 25-27 list all ordered pairs in the...Ch. 9.6 - Exercises 25-27 list all ordered pairs in the...Ch. 9.6 - What is the covering relation of the partial...Ch. 9.6 - What is the covering relation of the partial...Ch. 9.6 - What is the covering relation of the partial...Ch. 9.6 - w that a finite poset can be reconstructed from...Ch. 9.6 - wer these questions for the partial order...Ch. 9.6 - wer these questions for the poset ({3, 5,9, 15,...Ch. 9.6 - wer these questions for the poset ({2, 4, 6, 9,...Ch. 9.6 - wer these questions for the poset ({{1}, {2}, {4},...Ch. 9.6 - Prob. 36ECh. 9.6 - Show that lexicographic order is a partial...Ch. 9.6 - w that lexicographic order is a partial ordering...Ch. 9.6 - Suppose that (S,1) and (T,2) are posets. Show...Ch. 9.6 - a) Show that there is exactly one greatest element...Ch. 9.6 - a) Show that there is exactly one maximal element...Ch. 9.6 - a) Show that the least upper bound of a set in a...Ch. 9.6 - Determine whether the posets with these Hasse...Ch. 9.6 - Prob. 44ECh. 9.6 - Show that every nonempty finite subset of a...Ch. 9.6 - Show that if the poset (S,R) is a lattice then the...Ch. 9.6 - a company, the lattice model of information flow...Ch. 9.6 - Prob. 48ECh. 9.6 - Show that the set of all partitions of a set S...Ch. 9.6 - Show that every totally ordered set is a lattice.Ch. 9.6 - Show that every finite lattice has a least element...Ch. 9.6 - Give an example of an infinite lattice with a)...Ch. 9.6 - Prob. 53ECh. 9.6 - ermine whether each of these posets is...Ch. 9.6 - Prob. 55ECh. 9.6 - Show that dense poset with at least two elements...Ch. 9.6 - Show that the poset of rational numbers with the...Ch. 9.6 - Show that the set of strings of lowercase English...Ch. 9.6 - Prob. 59ECh. 9.6 - w that a finite nonempty poset has a maximal...Ch. 9.6 - Find a compatible total order for the poset with...Ch. 9.6 - d a compatible total order for the divisibility...Ch. 9.6 - Find all compatible total orderings for the poset...Ch. 9.6 - Find all compatible total orderings for the poset...Ch. 9.6 - Find all possible orders for completing the tasks...Ch. 9.6 - Schedule the tasks needed to build a house, by...Ch. 9.6 - Prob. 67ECh. 9 - Prob. 1RQCh. 9 - a) What is a reflexive relation? b) What is a...Ch. 9 - e an example of a relation on the set {1, 2,3,4}...Ch. 9 - a) How many reflexive relations are there on a set...Ch. 9 - a) Explain how ann-ary relation can be used to...Ch. 9 - a) Explain how to use a zero-one matrix to...Ch. 9 - a) Explain how to use a directed graph to...Ch. 9 - a) Define the reflexive closure and the symmetric...Ch. 9 - a) Define the transitive closure of a relation. b)...Ch. 9 - a) Define an equivalence relation. b) Which...Ch. 9 - a) Show that congruence modulo in is an...Ch. 9 - a) What are the equivalence classes of an...Ch. 9 - lain the relationship between equivalence...Ch. 9 - a) Define a partial ordering. b) Show that the...Ch. 9 - Explain how partial orderings on the...Ch. 9 - a) Explain how to construct the Hasse diagram of a...Ch. 9 - a) Define a maximal element of a poset and the...Ch. 9 - Prob. 18RQCh. 9 - a) Show that every finite subset of a lattice has...Ch. 9 - a) Define a well-ordered set. b) Describe an...Ch. 9 - Let S be the set of all stings of English leers....Ch. 9 - struct a relation on the set {a,b, c, d} that is...Ch. 9 - Show that the relationRonZZdefined by (a, b)R(c,...Ch. 9 - w that a subset of an antisymmetric relation is...Ch. 9 - LetRbe a reflexive relation on a setA. Show...Ch. 9 - Suppose thatR1andR2are reflexive relations on a...Ch. 9 - pose thatR1andR2are reflexive relations on a...Ch. 9 - Suppose that R is a symmetric relation on a set A....Ch. 9 - R1andR2be symmetric relations. IsR1R2also...Ch. 9 - A relationRis called circular ifaRbandbRcimply...Ch. 9 - Show that a primary key in ann-ary relation is a...Ch. 9 - Is the primary key in ann-ary relation also a...Ch. 9 - Show that the reflexive closure of the symmetric...Ch. 9 - Rbe the relation on the set of all mathematicians...Ch. 9 - a) Give an example to show that the transitive...Ch. 9 - a) LetSbe the set of subroutines of a computer...Ch. 9 - pose thatRandSare relations on a set A withRSsuch...Ch. 9 - Show that the symmetric closure of the union of...Ch. 9 - Devise an algorithm, based on the concept of...Ch. 9 - ch of these are equivalence relations on the set...Ch. 9 - How many different equivalence relations with...Ch. 9 - Show that{(x,y)xyQ}is an equivalence relation on...Ch. 9 - pose thatP1={A1,A2,....Am}andP2={B1,B2,....Bm}are...Ch. 9 - Prob. 24SECh. 9 - Prob. 25SECh. 9 - Let P(S) be thesetof all partitions of the set S....Ch. 9 - edule the tasks needed to cook a Chinese meal by...Ch. 9 - Find all chains in the posets with the Hass...Ch. 9 - Prob. 29SECh. 9 - Find an antichain with the greatest number of...Ch. 9 - Show that every maximal chain in a finite poset...Ch. 9 - Prob. 32SECh. 9 - w that in any group ofmn+1people there is either a...Ch. 9 - Prob. 34SECh. 9 - Prob. 35SECh. 9 - Prob. 36SECh. 9 - Prob. 37SECh. 9 - LetRbe a quasi-ordering and let S be the relation...Ch. 9 - w that the following properties hold for all...Ch. 9 - w that ifxandyare elements of a...Ch. 9 - w that ifLis a bounded lattice with upper bound 1...Ch. 9 - w that every finite lattice is bounded. A lattice...Ch. 9 - Give an example of a lattice that is not...Ch. 9 - Show that the lattice(P(S),)whereP(S) is the power...Ch. 9 - the lattice (Z+,)distributive? The complement of...Ch. 9 - Give an example of a finite lattice where at least...Ch. 9 - w that the lattice(P(S))whereP(S)is the power set...Ch. 9 - Show that ifLis a finite distributive lattice,...Ch. 9 - w that the game of Chomp with cookies arranged in...Ch. 9 - w that if(S,)has a greatest elementb,then a...Ch. 9 - Prob. 1CPCh. 9 - Prob. 2CPCh. 9 - Prob. 3CPCh. 9 - Prob. 4CPCh. 9 - Prob. 5CPCh. 9 - Prob. 6CPCh. 9 - Prob. 7CPCh. 9 - Prob. 8CPCh. 9 - Prob. 9CPCh. 9 - Given the matrix representing relation on a finite...Ch. 9 - Prob. 11CPCh. 9 - en the matrix representing a relation on a finite...Ch. 9 - Given the matrix representing a relation on a...Ch. 9 - Prob. 14CPCh. 9 - Prob. 15CPCh. 9 - Prob. 1CAECh. 9 - Prob. 2CAECh. 9 - Prob. 3CAECh. 9 - Prob. 4CAECh. 9 - d the transitive closure of a relation of your...Ch. 9 - pute the number of different equivalence relations...Ch. 9 - Prob. 7CAECh. 9 - Prob. 8CAECh. 9 - Prob. 9CAECh. 9 - Discuss the concept of a fuzzy relation. How are...Ch. 9 - cribe the basic principles of relational...Ch. 9 - Explain how the Apriori algorithm is used to find...Ch. 9 - Describe some applications of association rules in...Ch. 9 - Prob. 5WPCh. 9 - Prob. 6WPCh. 9 - Prob. 7WPCh. 9 - Prob. 8WPCh. 9 - Prob. 9WPCh. 9 - Prob. 10WPCh. 9 - Prob. 11WPCh. 9 - Prob. 12WP
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- how to construct the following same table?arrow_forwardThe following is known. The complete graph K2t on an even number of vertices has a 1- factorization (equivalently, its edges can be colored with 2t - 1 colors so that the edges incident to each vertex are distinct). This implies that the complete graph K2t+1 on an odd number of vertices has a factorization into copies of tK2 + K₁ (a matching plus an isolated vertex). A group of 10 people wants to set up a 45 week tennis schedule playing doubles, each week, the players will form 5 pairs. One of the pairs will not play, the other 4 pairs will each play one doubles match, two of the pairs playing each other and the other two pairs playing each other. Set up a schedule with the following constraints: Each pair of players is a doubles team exactly 4 times; during those 4 matches they see each other player exactly once; no two doubles teams play each other more than once. (a) Find a schedule. Hint - think about breaking the 45 weeks into 9 blocks of 5 weeks. Use factorizations of complete…arrow_forward. The two person game of slither is played on a graph. Players 1 and 2 take turns, building a path in the graph. To start, Player 1 picks a vertex. Player 2 then picks an edge incident to the vertex. Then, starting with Player 1, players alternate turns, picking a vertex not already selected that is adjacent to one of the ends of the path created so far. The first player who cannot select a vertex loses. (This happens when all neighbors of the end vertices of the path are on the path.) Prove that Player 2 has a winning strategy if the graph has a perfect matching and Player 1 has a winning strategy if the graph does not have a perfect matching. In each case describe a strategy for the winning player that guarantees that they will always be able to select a vertex. The strategy will be based on using a maximum matching to decide the next choice, and will, for one of the cases involve using the fact that maximality means no augmenting paths. Warning, the game slither is often described…arrow_forward
- Let D be a directed graph, with loops allowed, for which the indegree at each vertex is at most k and the outdegree at each vertex is at most k. Prove that the arcs of D can be colored so that the arcs entering each vertex must have distinct colors and the arcs leaving each vertex have distinct colors. An arc entering a vertex may have the same color as an arc leaving it. It is probably easiest to make use of a known result about edge coloring. Think about splitting each vertex into an ‘in’ and ‘out’ part and consider what type of graph you get.arrow_forward3:56 wust.instructure.com Page 0 Chapter 5 Test Form A of 2 - ZOOM + | Find any real numbers for which each expression is undefined. 2x 4 1. x Name: Date: 1. 3.x-5 2. 2. x²+x-12 4x-24 3. Evaluate when x=-3. 3. x Simplify each rational expression. x²-3x 4. 2x-6 5. x²+3x-18 x²-9 6. Write an equivalent rational expression with the given denominator. 2x-3 x²+2x+1(x+1)(x+2) Perform the indicated operation and simplify if possible. x²-16 x-3 7. 3x-9 x²+2x-8 x²+9x+20 5x+25 8. 4.x 2x² 9. x-5 x-5 3 5 10. 4x-3 8x-6 2 3 11. x-4 x+4 x 12. x-2x-8 x²-4 ← -> Copyright ©2020 Pearson Education, Inc. + 5 4. 5. 6. 7. 8. 9. 10. 11. 12. T-97arrow_forwardplease work out more details give the solution.arrow_forward
- Problem #5 Suppose you flip a two sided fair coin ("heads" or "tails") 8 total times. a). How many ways result in 6 tails and 2 heads? b). How many ways result in 2 tails and 6 heads? c). Compare your answers to part (a) and (b) and explain in a few sentences why the comparison makes sense.arrow_forwardBurger Dome sells hamburgers, cheeseburgers, french fries, soft drinks, and milk shakes, as well as a limited number of specialty items and dessert selections. Although Burger Dome would like to serve each customer immediately, at times more customers arrive than can be handled by the Burger Dome food service staff. Thus, customers wait in line to place and receive their orders. Burger Dome analyzed data on customer arrivals and concluded that the arrival rate is 30 customers per hour. Burger Dome also studied the order-filling process and found that a single employee can process an average of 44 customer orders per hour. Burger Dome is concerned that the methods currently used to serve customers are resulting in excessive waiting times and a possible loss of sales. Management wants to conduct a waiting line study to help determine the best approach to reduce waiting times and improve service. Suppose Burger Dome establishes two servers but arranges the restaurant layout so that an…arrow_forwardPEER REPLY 1: Choose a classmate's Main Post. 1. Indicate a range of values for the independent variable (x) that is reasonable based on the data provided. 2. Explain what the predicted range of dependent values should be based on the range of independent values.arrow_forward
- Note: A waiting line model solver computer package is needed to answer these questions. The Kolkmeyer Manufacturing Company uses a group of six identical machines, each of which operates an average of 18 hours between breakdowns. With randomly occurring breakdowns, the Poisson probability distribution is used to describe the machine breakdown arrival process. One person from the maintenance department provides the single-server repair service for the six machines. Management is now considering adding two machines to its manufacturing operation. This addition will bring the number of machines to eight. The president of Kolkmeyer asked for a study of the need to add a second employee to the repair operation. The service rate for each individual assigned to the repair operation is 0.50 machines per hour. (a) Compute the operating characteristics if the company retains the single-employee repair operation. (Round your answers to four decimal places. Report time in hours.) La = L = Wa = W =…arrow_forward10 20 30 y vernier protractor scales. 60 30 0 30 60 40 30 20 10 0 30 60 0 10. Write the complement of each of the following angles. a. 67° b. 17°41' 11. Write the supplement of each of the following angles. a.41° b.99°32' 30 60 C. 20 10 20 90 60 30 69 30 30 40 50 c. 54°47' 53" 0 30 60 c. 103°03'27" 12. Given: AB CD and EF GH. Determine the value of each angle, 21 through /10, to the nearer minute. A- 25 21 = 22 = 23 = 24 = 25 = 46= 27 = C 28 = 29 = 210 = E 26 22 210 81°00' 29 4 142°00' G H 94°40' B Darrow_forward5. For the function y-x³-3x²-1, use derivatives to: (a) determine the intervals of increase and decrease. (b) determine the local (relative) maxima and minima. (e) determine the intervals of concavity. (d) determine the points of inflection. (e) sketch the graph with the above information indicated on the graph.arrow_forward
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