DISCRETE MATHEMATICS LOOSELEAF
8th Edition
ISBN: 9781264309689
Author: ROSEN
Publisher: MCG
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Textbook Question
Chapter 9.2, Problem 31E
ermine whether there is a primary key for the relation inExample 3.
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Write the given third order linear equation as an equivalent system of first order equations with initial values.
Use
Y1 = Y, Y2 = y', and y3 = y".
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√ (3t¹ + 3 − t³)y" — y" + (3t² + 3)y' + (3t — 3t¹) y = 1 − 3t²
\y(3) = 1, y′(3) = −2, y″(3) = −3
(8) - (888) -
with initial values
Y
=
If you don't get this in 3 tries, you can get a hint.
The system of first order differential equations
y₁ = -4y1 - 1y2
y2 = 1y1 - 2y2
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yı(t) =
Y2(t) =
Question 2
1 pts
Let A be the value of the triple integral
SSS.
(x³ y² z) dV where D is the region
D
bounded by the planes 3z + 5y = 15, 4z — 5y = 20, x = 0, x = 1, and z = 0.
Then the value of sin(3A) is
-0.003
0.496
-0.408
-0.420
0.384
-0.162
0.367
0.364
Chapter 9 Solutions
DISCRETE MATHEMATICS LOOSELEAF
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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- Question 1 Let A be the value of the triple integral SSS₂ (x + 22) = 1 pts dV where D is the region in 0, y = 2, y = 2x, z = 0, and the first octant bounded by the planes x z = 1 + 2x + y. Then the value of cos(A/4) is -0.411 0.709 0.067 -0.841 0.578 -0.913 -0.908 -0.120arrow_forwardQ1 (9 points) Calculate the triple integral SSSE x³ y² z dV where E is the region bounded by z — y = 1, = z+y=1, z= 0, x = 0, and x = 1.arrow_forwardQ2 (9 points) 2 = y2 x² + y² dA where D is the region in the first quadrant 1, and x² + y² = 4. Using polar coordinates, calculate SS D bounded by y = x, x = 0, x² + y²arrow_forward
- Problem 2-6. Need help on why its 1.22arrow_forwardScenario: As a data analyst for a retail company, you are tasked with examining the relationship between televisions screen size, and prices. Your analysis will involve both correlation and regression methods to quantify and interpret this relationship Make a Scatterplot of screen size vs. price. Explain in one sentence, does there appear to be a positive or a negative correlation between price and screen size? Paste a snapshot of the plot here. Please do not copy paste. Question 1: What is the value of correlation coefficient between screen size and price? Discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship Estimate the relationship between screen size and price using a simple linear regression model and interpret the estimated coefficients. In your interpretation, tell the dollar amount by which price will change for each unit of increase in screen size. (The answer for the second part of this…arrow_forwardIn the xy-plane, the graphs of the linear function and the exponential function E both pass through the points (0,2) and (1,6) The function f is given by f(x) = L(x) - E(x). What is the maximum value of f? A 0.007 B 0.172 C 0.540 D 1.002arrow_forward
- Tasks: A company manufactures two electronic products: Chipsets and LCD. Each product contributes differently to the profit. The production process is subject to constraints related to labour, manufacturing space, raw materials, and production time. You are required to determine the optimal production quantities for each product to maximize profit: • Develop and formulate a Linear programming model for the variables and constraints from the above context as given in Table 1 & 2. Assume Right-Hand Side (R.H.S) values for all elements and find the maximum profit and optimal variable values using graphical method (40%). Table I Variables Chipsets Profit Per Unit Assume as per convenience and Model Fit Assume as per convenience and Model Fit dictions: On LCD Table II Constraints Labour Manufacturing Space Raw Materials Production Time Units No of Labors Square Meters Kilograms Minutes Identify the feasible region and construct the graph using the graphical method. Evaluate, present. Find…arrow_forwardvery time you conduct a hypothesis test, there are four possible outcomes of your decision to reject or not reject the null hypothesis: (1) You don’t reject the null hypothesis when it is true, (2) you reject the null hypothesis when it is true, (3) you don’t reject the null hypothesis when it is false, and (4) you reject the null hypothesis when it is false. Consider the following analogy: You are an airport security screener. For every passenger who passes through your security checkpoint, you must decide whether to select the passenger for further screening based on your assessment of whether he or she is carrying a weapon. Suppose your null hypothesis is that the passenger has a weapon. As in hypothesis testing, there are four possible outcomes of your decision: (1) You select the passenger for further inspection when the passenger has a weapon, (2) you allow the passenger to board her flight when the passenger has a weapon, (3) you select the passenger for further inspection when…arrow_forwardEKS C ALEKS - Kim Johnson - Ch 6S × 4 www-awy.aleks.com alekscgi/x/sl.exe/16_u-lgNs/kr7j8FB)--BjuvZG weRMign 4tCy83MpSgONH0-ovaPm-Zym e Chrome isn't your default browser Set as default Ch 6 Sec 4 Homework Question 4 of 4 (1 point) | Question Attempt: 2 of Unlimited ✓ 2 ✓ 3 = 4 Stress at work: In a poll conducted by the General Social Survey, 81% of respondents said that their jobs were sometimes or always stressful. Two hundred workers are chosen at random. Use the TI-84 Plus calculator as needed. Round your answer to at least four decimal places. (a) Approximate the probability that 155 or fewer workers find their jobs stressful. (b) Approximate the probability that more than 145 workers find their jobs stressful. (c) Approximate the probability that the number of workers who find their jobs stressful is between 154 and 172 inclusive. Part 1 of 3 The probability that 155 or fewer workers find their jobs stressful is 0.1207 Part 2 of 3 bility that more than 145 workers find their jobs…arrow_forward
- A case-control (or retrospective) study was conducted to investigate a relationship between the colors of helmets worn by motorcycle drivers and whether they are injured or killed in a crash. Results are given in the accompanying table. Using a 0.01 significance level, test the claim that injuries are independent of helmet color. Color of Helmet Black White Yellow Red Blue Controls (not injured) 499 373 32 159 79 Cases (injured 221 108 8 66 38 or killed) Click here to view the chi-square distribution table. Chi-square distribution table Area to the Right of the Critical Value Degrees of Freedom 0.995 0.99 0.975 0.95 0.90 0.10 0.05 0.025 0.01 0.005 C. Ho: Injuries and neimet color are dependent H₁: Injuries and helmet color are independent D. Ho: Whether a crash occurs and helmet color are dependent 1 0.001 0.004 0.016 2.706 3.841 5.024 6.635 7.879 2 0.010 0.020 0.051 0.103 0.211 4.605 5.991 7.378 9.210 10.597 3 0.072 0.115 0.216 0.352 0.584 6.251 7.815 9.348 11.345 12.838 4 0.207 0.297…arrow_forwardConduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion. A person drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: 28, 32, 46, 39, 29, 26. Use a 0.025 significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die? Click here to view the chi-square distribution table. The test statistic is (Round to three decimal places as needed.) Chi-square distribution table Area to the Right of the Critical Value Degrees of Freedom 0.995 0.99 0.975 0.95 0.90 0.10 0.05 0.025 0.01 0.005 1 0.001 0.004 0.016 2.706 3.841 5.024 6.635 2 0.010 0.020 0.051 0.103 0.211 4.605 5.991 7.378 9.210 7.879 10.597 3 0.072 0.115 0.216 0.352 0.584 6.251 7.815 9.348 11.345 12.838 4 0.207 0.297 0.484 0.711 1.064 7.779 9.488 11.143 13.277 14.860 5…arrow_forwardThe online clothing retailer e-Parel is conducting a study to estimate the average size of the orders placed by visitors to its website. The project manager desires a $60 bound on the error of estimation at 90% confidence. The population standard deviation is unknown, and a “best guess” of $175 is used as the planning value for σ. Use the Distributions tool to help you answer the questions that follow. 0123 Select a Distribution The z-value for a 90% confidence interval of the population mean is . In order to satisfy the requirement of a $60 bound on the error of estimation, a sample size no smaller than is needed.arrow_forward
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