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Discrete Mathematics Problems

Discrete Mathematics ProblemsWilliam F. KlostermeyerSchool of ComputingUniversity of North FloridaJacksonville, FL 32224E-mail: Preface31 Basics .. Truth Tables and Logical Equivalences .. Quantifiers .. Circuits .. 112 Sets133 Functions174 Integers and Matrices215 Direct Proofs .. Proofs by Contradiction .. Proofs by Induction .. 276 Basic Problems .. Graphs .. Directed Graphs .. Problems Requiring Proofs .. 357 Counting398 Other Relations .. Algorithm Analysis .. Recurrence Relations .. Generating Functions .. Boolean Algebra .. 47 Chapter 0 PrefaceThis booklet consists of problem sets for a typical undergraduate discretemathematics course aimed at computer science students.

problems. 1. Input two bits, x;y and output two bits representing x−y (1−1 = 00, 1−0 = 01, 0 −0 = 00, 0−1 = 11). 2. Input two bits x;y and output two bits representing the absolute value of x−y 3. Input three bits x;y;z and output one bit which is the majority of the three input bits

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