# Errata File For Discrete Mathematics For Computer Science-Books Pdf 20 Jan 2020 | 36 views | 0 downloads | 28 Pages | 216.82 KB

Share Pdf : Errata File For Discrete Mathematics For Computer Science

Download and Preview : Errata File For Discrete Mathematics For Computer Science

Report CopyRight/DMCA Form For : Errata File For Discrete Mathematics For Computer Science

## Transcription

should be 9 12 1 Terms Theorems and Algorithms 581. p xviii Appendix A 587,should be Appendix A Languages and Regular Sets. p xviii Appendix B 591,should be Appendix B Finite Automata. p xviii Add below Appendix B entry B 1 Exercises,p xx l 20 with the all the. should be with all the,p 5 l 27 Such sets are called a finite set. should be Such a set is called a finite set, p 7 l 8 The bold on A B if and only if A B and B A should be removed.
p 10 l 22 We need to show that there is some fixed integer of the form 2k0 3. for k0 N that can be written as j 2 3 for some choice of j N If such a. j existed we would have 2k0 3 j 2 3 In the case k0 0 the element j. would have to satisfy 3 j 2 3 or j 2 6 0 for 3 to be in B. Is better written as We must prove 3 6 B by showing 3 cannot be. written as j 2 3 for any j N If 3 B there exists a j0 N such that. 3 j02 3 If such a j0 existed we would have 3 j02 3 or j02 6 Since. no such j0 exists 3 6 B, p 10 l 27 One set can be a member of a second subset but not every element of. the first set need be an element of the second set. should be One set can be a member of a second subset but not every. element of the second set need be an element of the first set. p 16 l 29 Add line starting at left margin before end of theorem mark d This. part is left as an exercise for the reader, p 18 l 25 Place A under the first figure and B under the second. p 19 l 19 of both B and C,should be of either B or C. p 21 l 4 sometimes call the,should be sometimes called the. p 22 l 2 But then,should be Then, p 23 l 17 There should be a blank line after the end of theorem mark.
p 24 l 16 line should be aligned with the left margin and not indented. p 25 l 11 its converse its inverse and its contrapositive. should be converse if b then a its inverse if not a then not b and. its contrapositive if not b then not a,p 25 l 32 Equivalent statements. should be equivalent statements a is true if and only if b is true. p 27 l 17 Theorem 7 b,should be Theorem 7 b in Section 1 3 2. p 28 l 23 When n copies of the same set are used the resulting Cartesian product. X X X is the set of all ordered n tuples of elements in X denoted X n. should be When n copies of the same set are used the product is called. a Cartesian product The resulting Cartesian product X X X is the. set of all ordered n tuples of elements in X denoted X n. p 28 l 27 1 b,should be 1 b, p 28 l 27 Omit the sentence The product of two sets is sometimes referred to. as the Cartesian product, p 28 l 33 l 34 remove italics from the two italicized copies of combinatorial. p 29 l 18 The Absorption Law holds,should be The Absorption Law for Join holds.
p 29 l 19 Add The Absorption Law for Meet follows from Theorems 2 and 3 of. Section 1 3 1,p 28 l 32 design that is of a computer. should be design of a computer chip, p 32 l 27 In parts b m sentence should align at the left margin. p 35 l 4 5 6 The markers i ii and iii should be enclosed in parentheses. p 35 l 17 part c,should be Theorem 1 c,p 35 l 18 part a. should be Theorem 1 a,p 35 l 19 part b,should be Theorem 1 b. p 35 l 25 part a,should be Theorem 1 a,p 35 l 27 part b.
should be Theorem 1 b,p 37 l 10 Theorem 6,should be Theorem 6 a. p 40 l 3 add Theorem 3 after Three Sets,p 46 l 4 four should be replaced with 4. p 46 l 7 three should be replaced with 3,p 46 l 10 two should be replaced with 2. p 46 l 13 one should be replaced with 1,p 46 l 16 zero should be replaced with 0. p 47 l 20 Let n be any natural number for which the result is true. should be Assume the result is true for some natural number say n. p 49 l 15 Let,should be Assume, p 53 l 18 remove sentence The next result was referred to in the discussion of.
computer switches in Section 1 3 4 and will be proved several times in the book. using several different ideas, replace with If you think of the elements of a set as switches that each. can be set on or off the next result tells you how many different ways you can. choose a subset of switches such that each element is on. p 53 l 21 Remove The proof of,p 57 l 8 to be either. should be as either,p 57 l 40 as algorithm,should be as an algorithm. p 58 l 29 algorithm,should be algorithm,p 60 l 27 algorithm. should be algorithm, p 68 bottom part of Figure 1 18 should have no n0 1 n0 2 n0 3 and n0 4.
in the five boxes inside the large bottom box,p 68 l 9 p1 p2 pk. should be p1 p2 pk,p 68 l 15 16 17 there are five occurrences of m. should be replace occurrences of m with l, n k l where k 6 1 and l 6 1 It follows easily that 1 k n and that. 1 l n Hence by the inductive hypothesis k l T So k and l can be. p 72 l 1 5 7 remove 8 from the three lists,p 72 l 17 l 8. should have added l 8 where k represents the number of 3 cent stamps. and l the number of 8 cent stamps used to make n cents of postage. p 74 l 12 This case,should be The proof,p 76 l 21 remove do from the end of the line.
p 93 l 5 Base cases,should be Base cases,p 93 l 6 Closure rules. should be Closure rules,p 93 l 518 Base cases,should be Base cases. p 93 l 19 Closure rules,should be Closure rules,p 93 l 29 remove after Theorem 1 8. p 95 l 18 p q r p,should be p q r p,p 98 l 10 for these gates. should be for and gates,p 98 l 12 AN D OR,should be OR AN D.
p 98 l 22 in Figure 2 7 there are four occurrences of P that should be occurrences. p 99 l 1 In Figure 2 8 the labels A and B should be positioned over the symbols. for the gates as C is and not labelling inputs,p 103 l 19 p q and r. should be p q r,p 105 l 26 p qr p, should be p q r p and the truth values should be centered under. the rightarrow in r p,p 108 l 32 q and r,should be q and r. p 110 l 15 This Proof is left for Exercise 23,should be This is Exercise 23. p 111 l 17 if and only if,should be then,p 111 l 21 Theorem 2 5.
should be Theorem 3,p 113 l 13 Half adder,should be Two binary bits are added. p 115 l 14 be easier than another for someone reading the program to under. should be easier to understand for someone reading the program. p 116 l 13 1 should be 1 l 16 2 should be 2 l 21 3 should be 3. p 119 l 11 in the text,should be in the text Figure 2 11. p 120 l 8 the symbol should be the symbol, p 120 ll 28 40 This material should be placed on p 190 as it deals with equiva. lence relations that have not yet been introduced,p 121 l 30 from the other form. should be from any other form,p 123 l 34 Table 2 8 True Terms l2 p q r.
should be Table 2 8 True Terms l4 p q r,p 123 l 35 in the interpretations l3 p q r. should be in the interpretations l5 p q r, p 125 figure after l 3 the output of the top negation should not be x but x and. the output from the bottom negation should not be y but y. p 131 l 2 Example 12 above,should be Example 12,p 135 l 11 A formula such as x 3. should be A mathematical formula such as x 3,p 135 l 31 such as. should be such as the mathematical symbol for less than. p 135 l 32 from the universal set,should be from a universal set defined on R.
p 136 l 33 Add as a new paragraph just before l 33 that starts with Let i j N. When we allocate storage for an array in a programming language we have. an example of restricted quantification where the universal set is the set of all. memory locations accessible by a program We want to explore this idea about. allocating memory in the next example,p 138 l 4 Example 4 in Section 2 7 4 shows. should be Example 4 shows,p 138 l 19,x y P x y is logically equivalent to x y P x y. x y P x y is logically equivalent to x y P x y,p 138 l 31. d x y x y z x z z y,d x y x y z x z z y,p 139 l 12. x y x y x x z x y,x y x y z x z x y,p 140 l 8 Because should be Since.
p 140 l 10 Remove sentence How about x 2 2 2 3 1,p 140 l 29 that is that x and y. should be that is x and y,x P x Q x x P x x Q x,x P x Q x x P x x Q x. p 141 l 14 one cannot check,should be one cannot use testing to check. p 141 l 30 for limit N 2 down to 0,should be for limit N 2 down to 0 do. p 141 l 31 for position 0 up to limit,should be for position 0 up to limit do.
p 142 l 24 for limit N 2 down to 0,should be for limit N 2 down to 0 do. p 142 l 28 for position 0 up to limit,should be for position 0 up to limit do. p 145 l 44 d x y P x y Q x y zR x z,should be d x y P x y Q x y z R x z. p 146 l 23 for i 1 2 n,should be for i 0 to n 1 do. p 147 l 4 For t 1 to 2N 1,should be For t 1 to 2N 1 do.
p 147 l 6 For position 1 to 2N 1,should be For position 1 to 2N 1 do. p 148 l 13 2 9 1 Terms and Theorems,should be Terms Theorems and Algorithms. p 151 l 24 TRUE and FALSE,should be T RU E and F ALSE. p 152 l 12 TRUE and FALSE,should be T RU E and F ALSE. p 159 l 1 A binary relation is a set of ordered pairs. should be Let X be a set,p 159 l 1 on a set X,should be on X.
p 162 l 25 X1 X2 Xn,should be X1 X2 Xn,p 163 l 7 such that for any n1 n2 n3 A. should be for any n1 n2 n3 A, p 173 l 28 How is the relation IsAdjacentT o related to the relation InF rontOf. A person x is adjacent to a person y if x is the person in front of y or y is the. person after x Said another way x IsAdjacentT o y means that x is just in. front of or just behind y, should be A person x is adjacent to a person y if x is the person in front. of y or y is the person after x Said another way x IsAdjacentT o y means that. x is just in front of or just behind y How is the relation IsAdjacentT o related. to the relation InF rontOf,p 175 l 6 By Theorem 1 a relation. should be By Theorem 1 Section 3 4 1 a relation,p 175 l 21 reflexive and transitive closure.
should be reflexive and transitive closure, p 185 ll 29 31 from which one may read off the equivalence relation Theorem. 3 says that one can go from a partition to an equivalence relation from. should be from which one may read off the equivalence relation Theorem. 3 says that one can go from a partition to an equivalence relation from. p 186 l 23 By Theorem 3 in this section this relation. should be By Theorem 3 this relation,p 186 l 33 Figure 3 9 on page 187 is a Venn. should be Figure 3 9 is a Venn,p 189 l 30 Prove Theorem 1. should be Prove Theorem 1 in Section 3 6 1,p 190 l 1 Prove Theorem 4. should be Prove Theorem 4 in Section 3 6 2, p 191 l 12 reflexive transitive antisymmetric relation.
should be reflexive transitive and antisymmetric relation. p 194 l 2 U V X,should be U V X,p 194 l 5 U V W X,should be U V W X. p 194 ll 19 21 linear ordering or total ordering on X. should be linear ordering or total ordering on X,p 196 ll 4 5 set inclusion P X then 0 1. should be set inclusion on P X then 0 1,p 198 l 7 finite set X and let x X. should be finite set X and let x X, p 200 l 23 Partial order would be better as Partial order schedule for file. processing and email checking Possibly should be Figure designation and call. p 201 l 1 Linear order would be better as Partial order schedule embedded. in linear order,p 201 l 18 Examples 5 a and b are partial.
should be Examples 5 a and b in Section 3 8 1 are partial. p 202 l 12 Prove Theorem 1 a,should be Prove Theorem 1 a in Section 3 8 3. p 202 l 1226 Prove Theorem 2,should be Prove Theorem 2 in Section 3 8 4. p 206 l 13 in the relation R0 in Table 3 14,should be in the relation R0 in Table 3 15. p 209 First table labelled R S should be labelled R0. p 209 l 6 of text not in a box join of R and S on N ame. should be natural join of R and S on N ame, p 209 Second table labelled R S should be labelled R S. p 213 l 10 3 12 1 Summary,should be 3 12 1 Terms Theorems and Algorithms.
p 218 ll 1 7 Define the relation D on N so that n D m if and only if n m An. upper bound of two natural numbers in D is a natural number that both divide. The smallest such natural number is called the least upper bound and is denoted. as lub For example 6 is the least upper bound of 2 and 3 A lower bound of. two natural numbers in D is a naturally number that divides both numbers The. largest such natural number is called the greatest lower bound and is denoted. as glb For example the greatest lower bound of 4 and 6 is 2 Find. should be Let m n N m divides y denoted as m n if there exists an. integer j N such that m n n Let m n N such that m n An upper bound. of m and n is an integer j N such that m j and n j An upper bound always. exists as m n is an upper bound for m and n The smallest upper bound is. called the least upper bound denoted as lub m n Likewise a lower bound. of m and n is an integer j N such that j m and j n A lower bound always. exists as 1 is a lower bound for m and n The largest lower bound is called the. greatest lower bound denoted as glb m n For 4 and 6 glb 4 6 2 and. lub 4 6 12 Find,p 220 l 4 is seated at a chair,should be is seated in a chair. p 223 l 32 Example 4 1a the range of function, should be Example 1 a in Section 4 1 the range of function. p 225 Figure 4 2 The circles at the left end of the segments should be at the. right end of the segments, p 228 Figure 4 5 needs p q r changed to p q r as the third term. down in the middle output lines Also p q r changed to p q r in. the fifth term down in the middle output lines The final output shoul. computer switches in Section 1 3 4 and will be proved several times in the book using several di erent ideas replace with If you think of the elements of a set as switches that each can be set on or o the next result tells you how many di erent ways you can choose a subset of switches such that each element is on p 53 l 21 Remove The

## Related Books

###### Mastering Machine Learning with Python in Six Steps Mastering Machine Learning with Python in Six Steps Manohar Swamynathan Bangalore Karnataka India ISBN 13 pbk 978 1 4842 2865 4 ISBN 13 electronic 978 1 4842 2866 1

###### LNAI 3176 Unsupervised Learning Unsupervised Learning 73 often call the data could correspond to an image on the retina the pixels in a camera or a sound waveform It could also correspond to less obviously sensory data for example the words in a news story or the list of items in a supermarket

###### UNSUPERVISED LEARNING AND CLUSTERING Unsupervised learning can be thought of as finding patterns in the data above and beyond what would be considered pure unstructured noise How does it compare to supervised learning With unsupervised learning it is possible to learn larger and more complex models than with supervised learning This is because in supervised learning one is trying to find the connection between two sets of

###### DSC TX10 TX100 TX100V Cyber shot User Guide Sony HDMI Resolution DSC TX100 TX100V only CTRL FOR HDMI Housing DSC TX10 only USB Connect Setting USB Power Supply LUN Setting Download Music Empty Music GPS setting DSC TX100V only GPS assist data DSC TX100V only TransferJet Eye Fi Power Save Memory Card Tool Internal Memory Tool Format Create REC Folder Change REC Folder Delete REC Folder Copy File Number 9 Clock Settings Area

###### Digital Still Camera DSC RX100M4 Sony Digital Still Camera DSC RX100M4 How to Use Before Use Names of parts Checking the camera and the supplied items 1 Identifying parts 2 Icons and indicators List of icons on the screen 3 Using the strap Using the wrist strap 4 Using the shoulder strap sold separately 5 Adjusting the viewfinder Adjusting the viewfinder diopter adjustment 6 In Camera guide About the In Camera

###### Digital Still Camera DSC HX90V DSC HX90 Sony Digital Still Camera DSC HX90V DSC HX90 How to Use Before Use Names of parts Checking the camera and the supplied items 1 Identifying parts 2 Icons and indicators List of icons on the screen 3 Using the strap Using the wrist strap 4 Adjusting the viewfinder Adjusting the viewfinder diopter adjustment 5 In Camera guide About the In Camera Guide 6 About the shooting advice 7

###### Faune PACA Publication n 59 Faune PACA Publication n 59 Inventaires des papillons de jour odonates et orthopt res men s sur la R serve Naturelle R gionale des Partias Hautes Alpes Juin 2016 www faune paca org Le site des naturalistes de la r gion PACA

###### tat des lpo fr ###### DSC T33 Diagramasde com Sony EMCS Co 2004K1600 1 2004 11 9 876 788 31 Published by DI Technical Support Section DSC T33 LEVEL 2 DSC T33 This Service Manual shows only the difference from DSC T3 Refer to the Service Manual Level2 9 876 764 31 of DSC T3 also for repair All of the accessories disassembly procedure exploded views of the DSC T33 are shown

###### La Liste rouge des esp ces menac es en France papillons de jour libellules demoiselles et phasmes soit au total 165 esp ces de la faune r unionnaise Ce travail a t r alis par le Comit fran ais de l UICN et le Mus um national d Histoire naturelle en collaboration avec de nombreuses organisations locales L tat des lieux fait appara tre un certain nombre

###### AS 3740 2004 Waterproofing of wet areas within residential Waterproofing of wet areas within residential buildings AS 3740 This is a free 8 page sample Access the full version online This Australian Standard was prepared by Committee BD 038 Wet Areas in Buildings It was approved on behalf of the Council of Standards Australia on 20 February 2004 and published on 15 April 2004 The following are represented on Committee BD 038 Architectural