DISCRETE MATH8th EditionROSEN Publisher: MCG CUSTOMISBN: 9781266712326
DISCRETE MATH
Solutions for DISCRETE MATH
Problem 2E:
Use a proof by cases to show that 10 is not the square of a positive integer. [Hint: Consider two...Problem 3E:
Use a proof by cases to show that 100 is not the cube of a positive integer. [Hint: Consider two...Problem 4E:
Prove that there are no positive perfect cubes less than 1000 that are the sum of the cubes of two...Problem 5E:
Prove that ifxandyare real numbers, thenmax(x,y)+min(x+y)=x+y . [Hint: Use a proof by cases, the two...Problem 6E:
Use a proof by cases to show thatmin(a,min(b,c))=min(min(a,b),c) whenevera,b, andcare real numbers.Problem 8E:
Prove using the notion of without loss of generality that5x+5y an odd integer whenxandyare integers...Problem 9E:
Prove the triangle inequality, which states that ifxandyare real numbers, then|x/+|y//|x+y|...Problem 10E:
Prove that there is a positive integer that equals the sum of the positive integers not exceeding...Problem 11E:
Prove that there are 100 consecutive positive integers that are not perfect squares. Is your proof...Problem 12E:
Prove that either210500+15 or210500+16 is not a perfect square. Is your proof constructive or...Problem 13E:
Prove that there exists a pair of consecutive integers such that one of these integers a perfect...Problem 14E:
Show that the product of two of the numbers65100082001+317779121292399+22001 and24449358192+71777 is...Problem 15E:
Prove or disprove that there is a rational numberxand an irrational numberysuch thatxyis irrational.Problem 17E:
Show that each of these statements can be used to express the fact that there is a unique...Problem 18E:
Show that ifa,b, andcare real numbers anda0 , then there is a unique solution of the equationx+b=c .Problem 19E:
Suppose thataandbare odd integers with ab . Show there is a unique integercsuch that|ac|=|bc| .Problem 20E:
Show that ifris an irrational number, there is a unique integernsuch that the distance...Problem 21E:
Show that ifnis an odd integer, then there is a unique integerksuch thatnis the sum ofk2 andk+3 .Problem 24E:
Use forward reasoning to show that ifxis a nonzero real number, thenx2+1/x22 . [Hint:Start with the...Problem 26E:
Thequadratic meanof two real numbersxandyequals(x2+y2)/2 . By computing the arithmetic and quadratic...Problem 27E:
Write the numbers 1, 2, …,2non the black board, wherenis an integer. Pick any two of the...Problem 28E:
Suppose that five ones and four zeros are arranged around a circle. Between any two equal bits you...Problem 30E:
Formulate a conjecture about the final two decimal digits of the square of an integer. Prove your...Problem 34E:
Prove that there are infinitely many solutions in positive integersx,y, andzto the equationx2+y2=z2...Problem 36E:
Prove that 23 is irrational.Problem 38E:
Prove that between every rational number and every irrational number there is an irrational number.Problem 39E:
LetS=x1y1+x2y2++xnyn , wherex1,x2...,xn andy1,y2..,yn are orderings of two different sequences of...Problem 40E:
Prove or disprove that if you have an 8-gallon jug of water and two empty jugs with capacities of 5...Problem 43E:
Prove or disprove that you can use to tile the standard checkerboard with two adjacent corners...Problem 44E:
Prove or disprove that you can use dominoes to tile a standard checkerboard with all four corners...Problem 45E:
Prove that you can use dominoes to tile a rectangular checkerboard with an even number of squares.Problem 46E:
Prove or disprove that you can use dominoes to tile a55 checkerboard with three corners removed.Problem 47E:
Use a proof by exhaustion to show that a tiling using dominoes of a44 checkerboard opposite corners...Problem 48E:
Prove that when a white square and a black square are removed from an88 checkerboard (colored as in...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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