DISCRETE MATH8th EditionROSEN Publisher: MCG CUSTOMISBN: 9781266712326
DISCRETE MATH
Solutions for DISCRETE MATH
Problem 4E:
Find the domain and range of these functions. Note that in each case, to find the domain, determine...Problem 5E:
Find the domain and range of these functions. Note that in each case, to find the domain, determine...Problem 6E:
Find the domain and range of these functions. the function that assigns to each pair of positive...Problem 7E:
Find the domain and range of these functions. the function that assigns to each pair of positive...Problem 9E:
Find these values. 34 78 34 78 3 1 12+32 1252Problem 11E:
Which functions in Exercise 10 are onto? Determine whether each of these functions from {a,b,c,d} to...Problem 12E:
Determine whether each of these functions from Z to Z is one-to-one. f(n)=n1 f(n)=n2+1 f(n)=n3...Problem 14E:
Determine whether f:ZZZ is onto if f(m,n)=2mn . f(m,n)=m2n2 . f(m,n)=m+n+1 . f(m,n)=|m||n| ....Problem 15E:
Determine whether the function f:ZZZ is onto if f(m,n)=m+n . f(m,n)=m2+n2 . f(m,n)=m . f(m,n)=|n| ....Problem 16E:
Consider these functions from the set of students in a discrete mathematics class. Under what...Problem 17E:
Consider these functions from the set of teachers in a school. Under what conditions is the function...Problem 18E:
Specify a codomain for each of the functions in Exercise 16. Under what conditions is each of these...Problem 19E:
Specify a codomain for each of the functions in Exercise 17. Under what conditions is each of the...Problem 21E:
Give an explicit formula for a function from the set of integers to the set of positive integers...Problem 22E:
Determine whether each of these functions is a bijection from R to R. f(x)=3x+4 f(x)=3x2+7...Problem 23E:
Determine whether each of these functions is a bijection from R to R. f(x)=2x+1 f(x)=x2+1 f(x)=x3...Problem 24E:
Let f:RR and let f(x)0 for all xR . Show that f(x) is strictly increasing if and only if the...Problem 25E:
Let f:RR and 1et f(x)0 for all xR . Show that f(x) is strictly decreasing if and only if the...Problem 26E:
Prove that a strictly increasing function from R to itself is one-to-one. Give an example of an...Problem 28E:
Show that the function f(x)=ex from the set of real numbers to the set of real numbers is not...Problem 31E:
Let f(x)=x2/3 . Find f(S) if S={2,1,0,1,2,3} S={0,1,2,3,4,5} S={1,5,7,11} S={2,6,10,14}Problem 34E:
Suppose that g is a function from A to B and f is a function from B to C. Prove each of these...Problem 40E:
Let f(x)ax+b and g(x)=cx+d , where a, b, c, and d are constants. Determine necessary and sufficient...Problem 41E:
Show that the function f(x)ax+b from R to R, where a and b are constants with a0 is invertible, and...Problem 44E:
Let f be the function from R to R defined by f(x)=x2 . Find f1({1}) . f1({x0x1}) . f1({xx4}) .Problem 48E:
Show x+12 is the closest integer to the number x except when x is midway between two integers when...Problem 50E:
Show that if x is a real number, then xx=1 if x is not an integer and xx=0 if x is an integer.Problem 54E:
Show that if x is a real number and n is an integer, then xn if and only if xn . nx if and only if...Problem 56E:
Prove that if x is a real number, then x=x and x=x .Problem 61E:
How many bytes are required to encode n bits of data where n equals 7? 17? 1001? 28,800?Problem 62E:
How many ATM cells (described in Example 30) can be transmitted in 10 seconds over a link operating...Problem 63E:
Data are transmitted over a particular Ethernet network in blocks of 1500 octets (blocks of 8 bits)....Problem 64E:
Draw the graph of the function f(n)=1n2 from Z to Z.Problem 65E:
Draw the graph of the function f(x)=2x from R to R.Problem 66E:
Draw the graph of the function f(x)=x/2 from R to R.Problem 69E:
Draw graphs of each of these functions. f(x)=x+12 f(x)=2x+1 f(x)=x/3 f(x)=1/3 f(x)=x2+x+2 f(x)=2xx/2...Problem 71E:
Find the inverse function of f(x)=x3+1 .Problem 72E:
Suppose that f is an invertible function from Y to Z and g is an invertible function from X to Y....Problem 73E:
Let S be a subset of a universal set U. The characteristic function fS of S is the function from U...Problem 74E:
Suppose that f is a function from A to B, where A and B are finite sets with |A|=|B| . Show that f...Problem 75E:
Prove or disprove each of these statements about the floor and ceiling functions. x=x for all real...Problem 76E:
Prove or disprove each of these statements about the floor and ceiling functions. x=x for all real...Problem 78E:
Let x be a real number. Show that 3x=x+x+13+x+23 .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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