DISCRETE MATHEMATICS LOOSELEAF
8th Edition
ISBN: 9781264309689
Author: ROSEN
Publisher: MCG
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Chapter 9.2, Problem 35E
To determine
To calculate:
The support and confidence of the association rule
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On an assembly line, there are 3 "checkpoints" at which a widget is inspected for defects. Upon review of prior data, the following is noted:
The test for product integrity finds a problem 26% of the time
The test for product specifications finds a problem 19% of the time
The test for packaging consistency finds a problem 38% of the time
(It's not a particularly good assembly line!)
Assume for purposes of this problem, that all of the tests / checkpoint problems are independent of each other.
What is the probability that an error will be found by all of the tests?
What is the probability that an error will be found by any one of the tests? That is, a problem on the first, or second, or third test?
What is the probability that a problem will be found for the "packaging consistency" only?
What is the probability of finding an error of at least one of the tests? Hint: You can use your complement rule here.
According to a recent survey of adults, approximately 62% carry cash on a regular basis. The adults were also asked if they have children. Of the 46% who have children, 85% carry cash on a regular basis. Is carrying cash independent from having children in this sample?
No, P(carry cash) = P(carry cash|have children).
No, P(carry cash) ≠ P(carry cash|have children).
Yes, P(carry cash) = P(carry cash|have children).
Yes, P(carry cash) ≠ P(carry cash|have children).
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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- How does qualification of one tail test is done?arrow_forwardWhat are the 2 variables being correlated (or assumed correlated) in the Hypothesis Statement?arrow_forwardThe following table shows 1000 nursing school applicants classified according to scores made on a college entrance examination and the quality of the high. school from which they graduated, as rated by a group of educators: \begin{tabular}{1cccc} & \multicolumn {3}{c}{ Quality of High School ] & \\ \cline 2 4 Score & Poor & Average & - Superior & Total \\ \hline Low & 105 & 60 & 55 & 220 \\ Mediun & 70 & 175 & 145 & 390 \\ High & 25 & 65 & 300 & 390 \\ \hline Total & 200 & 300 & 500 & 1000 \\ \hline \end{tabular} Calculate the probability that an applicant picked at random from this group made a low score on the examination or graduated from a superior high school. $55 / 1000$ $55 / 200$ $665 / 1000$ $220 / 1000$ SS.SP.282arrow_forward
- Show that for 2² factorial experiment the main effects and interactions are mutually orthogonal.arrow_forwardData released by the Department of Education regarding the rate (percentage) of ninth-grade students who don't graduate in a certain year showed that, out of 50 states, 14 states had an increase in the dropout rate during the past 2 years. 17 states had a dropout rate of at least 30% during the past 2 years. 25 states had an increase in the dropout rate and/or a dropout rate of at least 30% during the past 2 years. (a) How many states had both a dropout rate of at least 30% and an increase in the dropout rate over the 2-year period? states (b) How many states had a dropout rate that was less than 30% but that had increased over the 2-year period? states Need Help? Read It Watch Itarrow_forward14, 14, 16, 12, 12, 14, 13, 16, 15, 14, 12, 15, 15, 14, 13, 13,12, 13, 10,13 Electronic ticketing allow passenger to not worry about a paper ticket, and it cost the airline companies less to handle than paper ticketing. however in recent time the airline have receive complaints from passengers regarding their eticket, particularly when cannecting flights and a change of airlines were involved. To investigates a problem an independent watchdog agency contacts a random sample of 20 airport and collected information on the number of complains the airport had with etickets for the month of March. At the 0.05 significance level, can the watchdog agency concludes the mean number of complains per airport is less than 15 per month. conduct a test of hypothesis and interprets the results. What is the decision rule and computes the value of so test statistics.arrow_forward
- A physiologist believes he has discovered a new steroid hormone that can control the blood glucose in mammals. In an experiment he injects laboratory rats with a small amount of this steroid hormone and, after a suitable waiting period measures the blood glucose level of the rats. In his twelve experimental rats he obtains the following levels of blood glucose {35,36,37,33,34,35,33,35,37,36,34,35}. From previous studies of thousands of normal, unmanipulated rats he knows that the mean (mu) blood glucose level in this species of rat (his laboratory population) is 31 and that the standard deviation is 4.12. Evaluate the hypothesis that this new steroid hormone affects blood glucose levels. Use an alpha-level of 0.01 for this analysis. Find the critical value:arrow_forwardA physiologist believes he has discovered a new steroid hormone that can control the blood glucose in mammals. In an experiment he injects laboratory rats with a small amount of this steroid hormone and, after a suitable waiting period measures the blood glucose level of the rats. In his twelve experimental rats he obtains the following levels of blood glucose {35,36,37,33,34,35,33,35,37,36,34,35}. From previous studies of thousands of normal, un-manipulated rats he knows that the mean (mu) blood glucose level in this species of rat (his laboratory population) is 31 and that the standard deviation is 4.12. Evaluate the hypothesis that this new steroid hormone affects blood glucose levels. Use an alpha-level of 0.01 for this analysis. State the null hypothesis:arrow_forwardA physiologist believes he has discovered a new steroid hormone that can control the blood glucose in mammals. In an experiment he injects laboratory rats with a small amount of this steroid hormone and, after a suitable waiting period measures the blood glucose level of the rats. In his twelve experimental rats he obtains the following levels of blood glucose {35,36,37,33,34,35,33,35,37,36,34,35}. From previous studies of thousands of normal, un-manipulated rats he knows that the mean (mu) blood glucose level in this species of rat (his laboratory population) is 31 and that the standard deviation is 4.12. Evaluate the hypothesis that this new steroid hormone decreases blood glucose levels. Use an alpha-level of 0.01 for this analysis.arrow_forward
- A physiologist believes he has discovered a new steroid hormone that can control the blood glucose in mammals. In an experiment he injects laboratory rats with a small amount of this steroid hormone and, after a suitable waiting period measures the blood glucose level of the rats. In his twelve experimental rats he obtains the following levels of blood glucose {35,36,37,33,34,35,33,35,37,36,34,35}. From previous studies of thousands of normal, un-manipulated rats he knows that the mean (mu) blood glucose level in this species of rat (his laboratory population) is 31 and that the standard deviation is 4.12. Evaluate the hypothesis that this new steroid hormone affects blood glucose levels. Use an alpha-level of 0.01 for this analysis. Is it a one-tailed (directional) test or a two-tailed test (nondirectional)?arrow_forwardData on the amount of the customers' shopping by using an account card and whether they decided to upgrade their account from silver status to platinum status after receiving the upgrade offer is shown in Table 2. Construct the k nearest neighbors scheme for predicting upgrades based on the data given in Table 2, and interpret the confusion matrix. According to the data given in part 1, estimate the probability of upgrade for each division of the purchase amount, using Bayes' theorem. Please provide your work in detail and include in-text citations. At least five (5) references are required for PA’s and CLA’sarrow_forwardChapter 6, Section 4-HT, Exercise 218 - MathPad Mind-Set MattersIn 2007 a Harvard psychologist set out to test her theory that ‘‘Mind-Set Matters.”1 She recruited 75 female maids2 working in different hotels to participate in her study, and informed 41 maids (randomly chosen) that the work they do satisfies the Surgeon General’s recommendations for an active lifestyle (which is true), giving the maids examples on how their work qualifies as good exercise. The other 34 maids were told nothing. After four weeks, the exercise habits of the two groups had not changed, but the informed group had lost an average of 1.79 lbs (s=2.88) and the uninformed group had lost an average of 0.2 lbs (s=2.32). The data are stored in MindsetMatters. Based on this study, does ‘‘Mind-Set Matter”? In other words, for maids, does simply thinking they are exercising more actually cause them to lose more weight?Click here for the dataset associated with this question.1Crum, A. and Langer, E.,…arrow_forward
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