Transcription of MATH208: DISCRETE MATHEMATICS
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MATH208: DISCRETE MATHEMATICS
U N D M AT H E M AT I C SM AT H 2 0 8 :D I S C R E T EM AT H E M AT I C SD E PA R T M E N T O F M AT H E M AT I C ST H E U N I V E R S I T Y O F N O R T H DA KOTAC opyright 2017 UND Mathematicspublished by department of mathematicsthe university of north 2005,2006,2007,2008,2009,2014,2015,2016, 2017 University of North Dakota MathematicsDepartmentPermission is granted to copy, distribute and/or modify this document under the terms of the GNU FreeDocumentation License, any later version published by the Free Software Foundation; withno Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included inthe section entitled "GNU Free Documentation License".Second corrected edition, Second printing: December2017 Contents1 Logical Connectives and Compound Implication and :If .. , then .. :.. if and only if .. table to propositional and .. , then .. normal and and to symbolic and basic laws of quantified of propositional with : Basic standard and universal and equality of set set string of by by a counterexample to disprove a a ordered digraph: domain= operations with relation using relation of a of with matrices: Boolean of class of a of an equivalence representation of an equivalence and Their of with DISCRETE domain and by0-1matrix or bipartite (injective) (surjective) of disc
7 10.2 Equivalence class of a relation 94 10.3 Examples 95 10.4 Partitions 97 10.5 Digraph of an equivalence relation 97 10.6 Matrix representation of an equivalence relation 97 10.7 Exercises 99 11 Functions and Their Properties 101 11.1 Definition of function 102 11.2 Functions with discrete domain and codomain 102 11.2.1 Representions by 0-1 matrix or bipartite graph 103
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