Boolean algebra and its applications

Title Page......Page 3 Copyright Page......Page 4 Preface......Page 5 Contents......Page 9 1-2 Element and set......Page 11 1-3 The combination of sets......Page 13 1-4 Venn diagrams......Page 15 1-5 Fundamental laws......Page 17 1-6 Expanding, factoring, and simplifying......Page 19 1-7 Properties of set inclusion......Page 22 1-8 Conditional equations......Page 25 1-9 Solution of equations......Page 29 1-10 The number of elements in a set......Page 30 2-2 Preliminary definitions......Page 35 2-3 Definition and properties of a Boolean algebra......Page 37 2-4 Disjunctive normal form......Page 43 2-5 Conjunctive normal form......Page 48 2-6 Representation of a Boolean algebra......Page 51 3-2 Propositions and definitions of symbols......Page 53 3-3 Truth tables......Page 57 3-5 Material implication......Page 62 3-6 Truth sets for propositions......Page 66 3-7 Quantifiers......Page 69 3-8 Valid arguments......Page 71 3-9 Indirect proofs......Page 76 3-10 Functionally complete sets of operations......Page 78 3-11 Special problems......Page 80 4-2 Definition of the algebraic symbols......Page 85 4-3 Simplification of circuits......Page 89 4-4 Non-series-parallel circuits......Page 93 4-5 Design of circuits from given properties......Page 100 4-6 Design of n-terminal circuits......Page 104 4-7 Symmetric functions and their circuits......Page 109 5-1 Introduction......Page 114 5-2 Basic relay control paths......Page 116 5-3 n-terminal circuits and the uses of transfer contacts......Page 120 5-4 Operate and hold paths......Page 126 5-5 Sequential circuits and sequence diagrams......Page 129 5-6 Design of sequential relay circuits from given conditions......Page 134 5-7 Special problems involving the design of relay circuits......Page 142 6-2 The binary number system......Page 145 6-3 Logical circuit elements......Page 148 6-4 Addition of binary numbers......Page 152 6-5 Subtraction of binary numbers.......Page 155 6-6 Accumulation......Page 157 6-7 Binary multiplication......Page 160 7-2 Event, sample space, probability......Page 163 7-3 Conditional probability......Page 167 7-4 Some aids to counting......Page 170 7-5 Bernoulli trials, binomial distribution......Page 173 ANSWERS TO SELECTED PROBLEMS......Page 178 INDEX......Page 189