DISCRETE MATH8th EditionROSEN Publisher: MCG CUSTOMISBN: 9781266712326
DISCRETE MATH
Solutions for DISCRETE MATH
Problem 4E:
Show that the additive inverse, or negative, of an even number is an even number using a direct...Problem 5E:
Prove that ifm+n andn+p are even integers, wherem,n, andpare integers, thenm+p is even. What kind of...Problem 7E:
Use a direct proof to show that every odd integer is the difference of two squares. [Hint: Find the...Problem 9E:
Use a proof by contradiction to prove that the sum of an irrational number and a rational number is...Problem 12E:
Prove or disprove that the product of a nonzero rational number and an irrational number is...Problem 13E:
Prove that ifxis irrational, then 1/xis irrational.Problem 16E:
Prove that ifx,y, andzare integers andx+y+z is odd, then at least one ofx,y, andzis odd.Problem 17E:
Use a proof by contraposition to show that ifx+y2 , wherexandyare real numbers, thenx1 ory1 .Problem 19E:
Show that ifnis an integer and n3+5 is odd, thennis even using a) a proof by contraposition. b) a...Problem 20E:
Prove that ifnis an integer and3n+2 is even, thennis even using a) a proof by contraposition. b) a...Problem 21E:
Prove the propositionP(0), whereP(n) is the proposition “Ifnis a positive integer greater than 1,n2n...Problem 22E:
Prove the propositionP(1), whereP(n) is the proposition "Ifnis a positive integer, then What kind of...Problem 23E:
LetP(n) be the proposition “Ifaandbare positive real numbers, then (a+b)nan+bn . Prove thatP(1) is...Problem 24E:
Show that if you pick three socks from a drawer containing just blue socks and black, you must get...Problem 26E:
Show that at least three of any 25 days chosen must fall in the same month of the year.Problem 27E:
Use a proof by contradiction to show that there is no rational numberrfor whichr3+r+1=0 . [Hint:...Problem 30E:
Prove that m2=n2 if and only ifm=n orm=n .Problem 31E:
Prove or disprove that ifmandnare integers such thatmn=1 , then eitherm=1 andn=1 , or elsem=1 and...Problem 32E:
Show that these three statements are equivalent, whereaandbare real numbers: (i)ais less thanb, (ii)...Problem 33E:
Show that these statements about the integerxare equivalent: (i)x+2 is even, (it)x+5 is odd, (iii)x2...Problem 34E:
Show that these statements about the real numberxare equivalent: (i)xis rational, (ii)x/2 is a...Problem 35E:
Show that these statements about the real numberxare equivalent: (i)xis irrational, (ii) x+2 is a...Problem 36E:
Is this reasoning for finding the solutions of the equation2x21=x correct?(1)2x21=x is...Problem 37E:
Is this reasoning for finding the solutions ofx+3=3x correct?(1)x+3=3x is given;(2)x+3=x26x+9 ,...Problem 38E:
Show that the propositionsp1,p2,p3, andp4can be shown to be equivalent by showing thatp1p4,p2p3 ,...Problem 39E:
Show that the propositionsp1,p2,p3,p4, andp5can be shown to be equivalent by proving that the...Problem 40E:
Find a counterexample to the statement that every positive integer can be written as the sum of the...Problem 41E:
Prove that at least real numbersa1,a2,…,anis greater than or equal to the average of these numbers....Problem 42E:
Use Exercise 41 to show that if the first 10 positive integers are placed around a circle, in any...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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