Discrete Mathematics and Its Applicatio...8th EditionROSEN Publisher: MCGISBN: 9781260501759
Discrete Mathematics and Its Applicatio...
Solutions for Discrete Mathematics and Its Applications
Problem 1E:
Which of these sentences are propositions? What are the truth values of those that are propositions?...Problem 2E:
Which of these are propositions? What are the truth values of those that are propositions? a) Do not...Problem 3E:
What is the negation of each of these propositions? a) Linda is younger than Sanjay. b) Mei makes...Problem 4E:
What is the negation of each of these propositions? a) Janice has more Facebook friends than Juan....Problem 5E:
What is the negation of each of these propositions? a) Mei has an MP3 player. b) There is no...Problem 6E:
What is the negation of each of these propositions? a) Jennifer and Teja are friends. b) There are...Problem 7E:
What is the negation of each of these propositions? a) Steve has more than 100 GB free disk space on...Problem 8E:
Suppose that Smartphone A has 256 MB RAM and 32 GB ROM, and the resolution of its camera is 8 MP;...Problem 9E:
Suppose that during the most recent fiscal year, the annual revenue of Acme Computer was 138 billion...Problem 10E:
Letpandqbe the propositions p:I bought a lottery ticket this week. q:I won the million dollar...Problem 11E:
Le p and q be the prepositions “Swimming at the New Jersey shore is allowed” and “Sharks have been...Problem 12E:
Le p and q be the prepositions “The election is decided” and “The votes have been counted,”...Problem 13E:
Let p and q be the propositions p: It is below freezing. q: It is snowing. Write these propositions...Problem 14E:
Let p, q, and r be the propositions p: You have the flu. q: You miss the final examination. r: You...Problem 15E:
Let p and q be the propositions p: You drive over 65 miles per hour. q: You get a speeding ticket....Problem 16E:
Let p, q, and r be the propositions p: You get an A on the final exam. q: You do every exercise in...Problem 17E:
Letp,q, andrbe the propositions p:Grizzly bears have been seen in the area. q:Hjång is safe on the...Problem 18E:
Determine whether these biconditionals are true or false. a)2+2=4if and only if 1+1=2. b)1+1=2if and...Problem 19E:
Determine whether each of these conditional statements is true or false. a) If1+1=2, then2+2=5. b)...Problem 20E:
Determine whether each of these conditional statements is true or false. a) If1+1=3, then unicorns...Problem 21E:
For each of these sentences, determine whether an inclusive or, or an exclusive or, is intended....Problem 22E:
For each of these sentences, determine whether an inclusive or, or an exclusive or, is intended....Problem 23E:
For each of these sentences, state what the sentence means if the logical connective or is an...Problem 24E:
Write each of these statements in the form "ifp, thenq" in English. [Hint:Refer to the list of...Problem 25E:
Write each of these statements in the form "ifp, thenq" in English [Hint:Refer to the list of common...Problem 26E:
Write each of these statements in the form "ifp, thenq" in English. [Hint:Refer to the list of...Problem 27E:
Write each of these propositions in the form "pif and only ifq" in English. a) If it is hot outside...Problem 28E:
Write each of these propositions in the form "pif and only ifq" in English. a) For you to get an A...Problem 29E:
State the converse, contrapositive, and inverse of each of these conditional statements. a) If it...Problem 30E:
State the converse, contrapositive, and inverse of each of these conditional statements. a) If it...Problem 31E:
How many rows appear in a truth table for each of these compound propositions? a)pp b)(pr)(qs)...Problem 32E:
How many rows appear in a truth table for each of these compound propositions? a)(qp)(pq) b)(pt)(ps)...Problem 33E:
Construct a truth table for each of these compound propositions. a)pp b)pp c)(pp)q d)(pq)(pq)...Problem 34E:
Construct a truth table for each of these compound propositions. a)pp b)pp c)p(pq) d)(pq)(pq)...Problem 35E:
Construct a truth table for each of these compound propositions. a)(pq)(pq) b)(pq)(pq) c)(pq)(pq)...Problem 36E:
Construct a truth table for each of these compound propositions. a)pp b)pp c)pq d)pq e)(pq)(pq)...Problem 37E:
Construct a truth table for each of these compound propositions. a)pq b)pq c)(pq)(pq) d)(pq)(pq)...Problem 38E:
Construct a truth table for each of these compound propositions. a)(pq)r b)(pq)r c)(pq)r d)(pq)r...Problem 39E:
Construct a truth table for each of these compound propositions. a)p(qr) b)p(qr) c)(pq)(pr)...Problem 40E:
Construct a truth table for((pq)r)s.Problem 41E:
Construct a truth table for(pq)(rs).Problem 42E:
Explain, without using a truth table, why(pq)(qr)(rp)is true whenp,q, andrhave the same truth value...Problem 43E:
Explain, without using a truth table, why(pqr)(pqr)is true when at least one ofp,q, andris true and...Problem 44E:
Ifp1,p2, ...,pnarenpropositions, explain why i=1n1j=i+1n(pipj) is true if and only if at most one...Problem 45E:
Use Exercise 44 to construct a compound proposition that is true if and only if exactly one of the...Problem 46E:
What is the value ofxafter each of these statements is encountered in a computer program,...Problem 47E:
Find the bitwiseOR, bitwiseAND, and bitwiseXORof each of these pairs of bit strings. a) 101 1110,...Problem 48E:
Evaluate each of these expressions. a)11000(0101111011) b)(0111110101)01000 c)(0101011011)01000...Problem 49E:
Fuzzy logicis used in artificial intelligence. In fuzzy logic, a proposition has a truth value that...Problem 50E:
Fuzzy logicis used in artificial intelligence. In fuzzy logic, a proposition has a truth value that...Problem 51E:
Fuzzy logicis used in artificial intelligence. In fuzzy logic, a proposition has a truth value that...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 Mathematics and Its Applications 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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