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