Introduction to Discrete Mathematics Via Logic and Proof (Instructor's Solution Manual) (Solutions)

Preface
	Topics Selected
	Intended Audiences
	Goals and Approach
	Prerequisites and Course Emphases
	For Students: Reading a Mathematics Text
Acknowledgements
List of Notations
	Logical Acronyms
Contents
1 Propositional Logic
	1.1 A Gentle Introduction to Logic and Proof
	1.2 Conjunction, Disjunction, and Negation
	1.3 Argument Semantics for Propositional Logic
	1.4 Conditional and Biconditional Sentences
	1.5 Introduction to Deduction; Rules for AND
	1.6 Elimination Rules for CONDITIONALS
	1.7 Introduction Rules for CONDITIONALS
	1.8 Proof by Contradiction: Rules for NOT
	1.9 Inference Rules for OR
2 First-Order Logic
	2.1 Symbolizing Sentences
	2.2 First-Order Logic: Syntax and Semantics
	2.3 Rules for Identity and Universal Quantifiers
	2.4 Rules for Existential Quantifiers
3 Mathematical Induction  and Arithmetic
	3.1 Mathematical Induction and Recursion
	3.2 Variations on Mathematical Induction and Recursion
	3.3 Recurrence Relations; Structural Induction
	3.4 Peano Arithmetic
	3.5 Divisibility
4 Basic Set Theory and Combinatorics
	4.1 Relations and Operations on Sets
	4.2 Collections of Sets and the Power Set
	4.3 Multiplicative Counting Principles
	4.4 Combinations
	4.5 Additive Counting Principles
5 Set Theory and Infinity
	5.1 Countably Infinite Sets
	5.2 Uncountably Infinite Sets
	5.3 Formal Set Theory and the Halting Problem
6 Functions and Equivalence Relations
	6.1 Functions and Their Properties
	6.2 Composite Functions and Inverse Functions
	6.3 Equivalence Relations and Partitions
	6.4 The Integers and Modular Arithmetic
7 Posets, Lattices, and Boolean Algebra
	7.1 Partially Ordered Sets
	7.2 Lattices
	7.3 From Boolean Lattices to Boolean Algebra
	7.4 Boolean Functions and Logic Circuits
	7.5 Representing Boolean Functions
	7.6 Simplifying Boolean Functions
8 Topics in Graph Theory
	8.1 Eulerian Trails
	8.2 Hamiltonian Paths
	8.3 Planar Graphs
	8.4 Coloring Graphs
*-21ptImage Credits
A Inference Rules for PL and FOL
*-16ptIndex
Index