DISCRETE MATH8th EditionROSEN Publisher: MCG CUSTOMISBN: 9781266712326
DISCRETE MATH
Solutions for DISCRETE MATH
Problem 14E:
ermine whetherx3isO(g(x))for each of these functionsg(x). g(x)=x2 g(x)=x3 g(x)=x2+x3 g(x)=x2+x4...Problem 15E:
Explain what it means for a function to be 0(1)Problem 16E:
w that iff(x)isO(x)thenf(x)isO(x2).Problem 17E:
Suppose thatf(x),g(x), andh(x)are functions such thatf(x)isO(g(x))andg(x)isO(h(x)). Show...Problem 18E:
kbe a positive integer. Show that1k+2k++nkisO(nk+1).Problem 20E:
To simplify:(3a5)3 27a15 Given information:(3a5)3. Calculation: We have(3a5)3 Take each factor to...Problem 21E:
ange the functionsn, 1000 logn,nlogn,2n!,2n,3n, andn2 /1, 000,000 in a list so that each function is...Problem 22E:
Arrange the functions(1.5)n,n100,(logn)3,nlogn,10n,(n!)2, andn99+n98in a list so that each function...Problem 23E:
Suppose that you have two different algorithms for solving a problem. To solve a problem of sizen,...Problem 24E:
Suppose that you have two different algorithms for solving a problem. To solve a problem of sizen,...Problem 25E:
Give as good a big-Oestimate as possible for each of these functions. (n2+8)(n+1) (nlogn+n2)(n3+2)...Problem 26E:
e a big-Oestimate for each of these functions. For the function g in your estimatef(x)isO(g(x)) ,...Problem 28E:
each function in Exercise 1, determine whether that function is(x)and whether it is(x). Determine...Problem 30E:
Show that each of these pairs of functions are of the same order. 3x+7,x 2x2+x7,x2 x+1/2,x...Problem 32E:
w thatf(x)andg(x)are functions from the set of real numbers to the set of real numbers,...Problem 34E:
Show that3x2+x+1is(3x2)by directly finding the constantsk,C1, andC2in Exercise 33. Express the...Problem 36E:
lain what it means for a function to be(1).Problem 48E:
ress the relationshipf(x)is(g(x))using a picture. Show the graphs of the functionsf(x)andCg(x) , as...Problem 50E:
w that iff(x)=anxn+an1xn1++a1x+a0, wherea0,a1,,an1, andanare real numbers andan0, thenf(x)is(xn)....Problem 54E:
w thatx5y3+x4y4+x3y5is(x3y3).Problem 55E:
w thatxyisO(xy).Problem 56E:
w thatxyis(xy).Problem 62E:
(Requires calculus) Prove or disprove that (2n)! isO(n!). The following problems deal with another...Problem 73E:
Show thatnlognisO(logn!).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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