DISCRETE MATH8th EditionROSEN Publisher: MCG CUSTOMISBN: 9781266712326
DISCRETE MATH
Solutions for DISCRETE MATH
Problem 1RQ:
a) Define the negation of a proposition. b) What is the negation of "This is a boring course"?Problem 2RQ:
a) Define (using truth tables) the disjunction, conjunction, exclusive or, conditional, and...Problem 3RQ:
a) Describe at least five different ways to the conditional statementpq in English. b) Define the...Problem 4RQ:
a) What does it mean for two propositions to be logically equivalent? b) Describe the different ways...Problem 5RQ:
(Depends on the Exercise Set inSection 1.3) a) Given a truth table, explain how to use disjunctive...Problem 6RQ:
What are the universal and existential quantifications of a predicateP(x)? What are their negations?Problem 7RQ:
a) What is the difference between the quantificationxyP(x,y) andyxP(x,y) , whereP(x,y) is a...Problem 8RQ:
Describe what is meant by a valid argument in propositional logic and show that the argument "If the...Problem 10RQ:
a) Describe what is meant by a direct proof, a proof by contraposition, and a proof by contradiction...Problem 11RQ:
a) Describe away to prove the bi-conditionalpq . b) Prove the statement: "The integer3n+2 is odd if...Problem 12RQ:
To prove that the statementp1,p2,p3, andp4are equivalent, is it sufficient to show that the...Problem 13RQ:
a) Suppose that a statement of the formxP(x) is false. How can this be proved? b) Show that the...Problem 14RQ:
What is the difference between a constructive and non-constructive existence proof? Give an example...Problem 15RQ:
What are the elements of a proof that there is a unique elementxsuch thatP(x), whereP(x) is a...Problem 1SE:
Letpbe the proposition "I do every exercise in this book" andqbe the proposition "I will get an A in...Problem 9SE:
Show that these statements are inconsistent: "If Miranda does not take a course in discrete...Problem 10SE:
Suppose that in a three-round obligato game, the teacher first gives the student the propositionpq ,...Problem 11SE:
Suppose that in a four-round obligato game, the teacher first gives the student the...Problem 12SE:
Explain why every obligato game has a winning strategy. Exercises 13 and 14 are set on the island of...Problem 14SE:
Suppose that you meet three people, Anita, Boris, and Carmen. What are Anita, Boris, and Carmen if...Problem 15SE:
(Adapted from [Sm78]) Suppose that on an island there are three types of people, knaves, and normals...Problem 16SE:
Show that ifSis a proposition, whereSis the conditional statement "IfSis true, then unicorns live,"...Problem 17SE:
Show that the argument premises "The tooth fry is a real person" and "The tooth fairy is not a real...Problem 18SE:
Suppose that the truth value of the propositionPiis T wheneveriis an odd positive integer and is F...Problem 20SE:
Let P(x) be the statement “Student x knows calculus” and letQ(y) be the statement “Classycontains a...Problem 21SE:
LetP(m,n) be the statement “mdividesn," where the domain for both variables consists of all positive...Problem 22SE:
Find a domain for the quantifiers in xy(xyz((z=x)(z=y))) such that this statement is true.Problem 25SE:
Use existential and universal quantifiers to express the statement "Everyone has exactly two...Problem 26SE:
The quantifiern denotes "there exists exactlyn," so thatnxP(x) means there exist exactlynvalues in...Problem 27SE:
Express each of these statements using existential and universal quantifiers and propositional...Problem 32SE:
Find the negations of these statements. a) If it snows today, then I will go skiing tomorrow. b)...Problem 33SE:
Express this statement using quantifiers: "Every student in class has taken some course in every...Problem 34SE:
Express statement using quantifiers: "There is a building on the campus of some college in the...Problem 38SE:
Prove that ifx3is irrational, thenxis irrational.Problem 41SE:
Prove that there exists an integermsuch thatm2101000 . Is your proof constructive or...Problem 43SE:
Disprove the statement that every positive integer is the sum of the cubes of eight nonnegative...Problem 44SE:
Disprove the statement that every positive integer is the sum of at most two squares and a cube of...Problem 46SE:
Assuming the truth of the theorem that states thatn is irrational whenevernis a positive integer...Problem 1CP:
Given the truth values of the propositionspandq, find the truth values of the conjunction,...Problem 6CP:
Given a portion of a checkerboard, look for tilings of this checkerboard with various types of...Problem 1CAE:
Look for positive integers that are not the sum of the cubes of nine different positive integers.Problem 2CAE:
Look for positive integers greater than 79 that are not the sum of the fourth powers of 18 positive...Problem 4CAE:
Try to find winning strategies for the game of Chomp for different initial configurations of...Problem 6CAE:
Find all the rectangles of 60 squares that can be tiled using every one of the 12 different...Problem 1WP:
Discuss logical paradoxes, including the paradox of Epimenides the Cretan, Jourdain's card paradox,...Problem 2WP:
Describe how fuzzy logic is being applied to practical applications. Consult one or more of the...Problem 3WP:
Describe some of the practical problems that can be modeled as satisfiability problems.Problem 5WP:
Describe some of the techniques that have been devised to help people solve Sudoku puzzles the use...Problem 6WP:
Describe the basic rules ofWFFN PROOF, The Game of Modern Logic, developed by Layman Allen. Give...Problem 7WP:
Read some of the writings of Lewis Carroll on symbolic logic. Describe in detail some of the models...Problem 8WP:
Extend the discussion of Prolog given inSection 1.4, explaining in more depth how Prolog employs...Problem 10WP:
"Automated theorem proving" is the task of using computers to mechanically prove theorems. Discuss...Problem 11WP:
Describe how DNA computing has been used to solve instances of the satisfiability problem.Problem 12WP:
Look up some of the incorrect proofs of famous open questions and open questions that were solved...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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