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Discrete Mathematics Problems

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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.

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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