DISCRETE MATH8th EditionROSEN Publisher: MCG CUSTOMISBN: 9781266712326
DISCRETE MATH
Solutions for DISCRETE MATH
Problem 3E:
Theorem 1 Let a, b, and c be integers, where ao . Then (i) if a|b and a|c, then a|(b+c); (ii) if...Problem 4E:
Prove that part (iii) of Theorem 1 is true. Let a,b, and c be integers, where ao . Then (i) if a|b...Problem 6E:
Show that if a, b, c, and d are integers, where a = o, such that a / c and b | d, then ab | cd.Problem 7E:
Show that if a, b, and c are integers, where ao , and co , such that ac | bc, then a | b.Problem 8E:
Prove or disprove that if a|bc, where a,b, and c are positive integers and ao then a | b or a | c.Problem 10E:
Prove that if a and b are nonzero integers, a divides b, and a+b is odd, then a is odd.Problem 11E:
Prove that if a is and integer that is not divisible by 3, then (a+1)(a+2) is divisible by 3.Problem 13E:
What are the quotient and remainder when a) 19 is divided by 7? b) -111 is divides by 11? c) 789 is...Problem 14E:
What are the quotient and remainder when 44 is divided by 8? 777 is divides by 21? -123 is divided...Problem 15E:
What time does a 12-hour clock read a) 80 hours after it reads 11:00? b) 40 hours before it reads...Problem 16E:
What time does a 24-hour clock read a) 100 hours after it reads 2:00? b) 45 hours before it reads...Problem 17E:
Suppose that a and b are integers, a4(mod13) , and b9(mod13) . Find the integer c with 0c2 such that...Problem 18E:
Suppose that a and b are integers, a11(mod19) and b3(mod19) . Find the integer c with oc18 such that...Problem 19E:
Show that if a and d are positive integers, then (a)divd=adivd if and only if d divides a.Problem 20E:
Prove or disprove that if a, b, and d are integers with d0 , then (a+b)divd=adivd+bdivd .Problem 24E:
Show that if a is and integer d is and integer greater than 1, then the quotient and remainder...Problem 25E:
Find a formula of the integer with smallest absolute value that is congruent to and integer a modulo...Problem 28E:
Find a div m and a mod m when a=111,m=99 . a=9999,m=101 . a=10299,m=999 . a=123456,m=1001 .Problem 29E:
Find a div m and a mod m when a=228,m=119 . a=9009,m=223 . a=10101,m=333 . a=765432,m=38271 .Problem 30E:
Find the integer a such that a43(mod23) and 22a0 . a17(mod29) and 14a14 . a11(mod21) and 90a110 .Problem 31E:
Find the integer a such that a15(mod27) and 26a0 . a24(mod31) and 15a15 . a99(mod41) and 100a140 .Problem 34E:
Decide whether each of these integers is congruent to 3 modulo 7. a) 37 b) 66 c) -17 d) -67Problem 35E:
Decide whether each of these integers is congruent to 5 modulo 17. a) 80 b) 103 c) -29 d) -122Problem 38E:
Find each of these values. a) (192mod41)mod9 b) ( 323mod13)2mod11 c) (72mod23)2mod31 d) (...Problem 39E:
Find each of these values. a) ( 992mod32)3mod15 b) (34mod17)2mod11 c) ( 193mod23)2mod31 d) (...Problem 40E:
Show that if a = b (mod m) and c= d (mod m), where a, b, c, d, and m are integers with m_>2, then...Problem 42E:
Show that if a, b, c, and m are integers such that m,c0 , and a=b(modm) , then ac=bc(modmc) .Problem 43E:
Find counter Examples to each of these statements about congruences. If ac = bc(mod m), where a,b,c...Problem 44E:
Show that if n is an integer then n20 or 1 (mod 4).Problem 48E:
Show that Zmwith addition modulo m, where m2 is an integer, satisfies the closure, associative, and...Problem 50E:
Show that the distributive property of multiplication over addition holds for Zm,where m2 is and...Problem 51E:
Write out the addition and multiplication tables for Z5 (where by addition and multiplication we...Browse All Chapters of This Textbook
Chapter 1 - The Foundations: Logic And ProofsChapter 1.1 - Propositional LogicChapter 1.2 - Applications Of Propositional LogicChapter 1.3 - Propositional EquivalencesChapter 1.4 - Predicates And QuantifiersChapter 1.5 - Nested QuantifiersChapter 1.6 - Rules Of InferenceChapter 1.7 - Indroduction To ProofsChapter 1.8 - Proof Methods And StrategyChapter 2 - Basic Structures: Sets, Functions, Sequences, Sums, And Matrices
Chapter 2.1 - SetsChapter 2.2 - Set OperationsChapter 2.3 - FunctionsChapter 2.4 - Sequences And SummationsChapter 2.5 - Cardinality Of SetsChapter 2.6 - MatricesChapter 3 - AlgorithmsChapter 3.1 - AlgorithmsChapter 3.2 - The Growth Of FunctionsChapter 3.3 - Complexity Of AlgorithmsChapter 4 - Number Theory And CryptographyChapter 4.1 - Divisibility And Modular ArithmeticChapter 4.2 - Integer Representations And AlgorithmsChapter 4.3 - Primes And Greatest Commom DivisiorsChapter 4.4 - Solving CongruencesChapter 4.5 - Applications Of CongruencesChapter 4.6 - CryptographyChapter 5 - Induction And RecursionChapter 5.1 - Mathematical InductionChapter 5.2 - Strong Induction And Well-orderingChapter 5.3 - Recursive Definitions And Structural InductionChapter 5.4 - Recursive AlgorithmsChapter 5.5 - Program CorrectnessChapter 6 - CountingChapter 6.1 - The Basics Of CountingChapter 6.2 - The Pigeonhole PrincipleChapter 6.3 - Permutations And CombinationsChapter 6.4 - Binomial Coefficients And IdentitiesChapter 6.5 - Generalized Permutations And CombinationsChapter 6.6 - Generating Permutations And CombinationsChapter 7 - Discrete ProbabilityChapter 7.1 - An Introduction To Discrete ProbabilityChapter 7.2 - Probability TheoryChapter 7.3 - Bayes' TheoremChapter 7.4 - Expected Value And VarianceChapter 8 - Advanced Counting TechniquesChapter 8.1 - Applications Of Recurrence RelationsChapter 8.2 - Solving Linear Recurrence RelationsChapter 8.3 - Divide-and-conquer Algorithms And Recurrence RelationsChapter 8.4 - Generating FunctionsChapter 8.5 - Inclusion-exclusionChapter 8.6 - Applications Of Inclusion-exclusionChapter 9 - RelationsChapter 9.1 - Relations And Their PropertiesChapter 9.2 - N-ary Relations And Their ApplicationsChapter 9.3 - Representing RelationsChapter 9.4 - Closures Of RelationsChapter 9.5 - Equivalence RelationsChapter 9.6 - Partial OrderingsChapter 10 - GraphsChapter 10.1 - Graphs And Graph ModelsChapter 10.2 - Graph Terminology And Special Types Of GraphsChapter 10.3 - Representing Graphs And Graph IsomorphismChapter 10.4 - ConnectivityChapter 10.5 - Euler And Hamilton PathsChapter 10.6 - Shortest-path ProblemsChapter 10.7 - Planar GraphsChapter 10.8 - Graph ColoringChapter 11 - TreesChapter 11.1 - Introduction To TreesChapter 11.2 - Applications Of TreesChapter 11.3 - Tree TraversalChapter 11.4 - Spanning TreesChapter 11.5 - Minimum Spanning TreesChapter 12 - Boolean AlgebraChapter 12.1 - Boolean FunctionsChapter 12.2 - Representing Boolean FunctionsChapter 12.3 - Logic GatesChapter 12.4 - Minimization Of CircuitsChapter 13 - Modeling ComputationChapter 13.1 - Languages And GrammarsChapter 13.2 - Finite-state Machines With OutputChapter 13.3 - Finite-state Machines With No OutputChapter 13.4 - Language RecognitionChapter 13.5 - Turing MachinesChapter A - Appendices
Sample Solutions for this Textbook
We offer sample solutions for DISCRETE MATH homework problems. See examples below:
Chapter 1, Problem 1RQA set P is a subset of Q if each element of P is also the element of Q. We have to show that P is a...Chapter 3, Problem 1RQChapter 4, Problem 1RQChapter 5, Problem 1RQChapter 6, Problem 1RQChapter 7, Problem 1RQChapter 8, Problem 1RQIn mathematics, a binary relation on a set A is a set of ordered pairs of elements of A defined as...
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