## Discrete Structures, Logic, and ComputabilityThoroughly updated, the new Third Edition of Discrete Structures, Logic, and Computability introduces beginning computer science and computer engineering students to the fundamental techniques and ideas used by computer scientists today, focusing on topics from the fields of mathematics, logic, and computer science itself. Dr. Hein provides elementary introductions to those ideas and techniques that are necessary to understand and practice the art and science of computing. The text contains all the topics for discrete structures in the reports of the IEEE/ACM Joint Task Force on Computing Curricula for computer science programs and for computer engineering programs. |

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### Contents

Elementary Notions and Notations | 1 |

Facts about Functions | 75 |

Construction Techniques | 133 |

Equivalence Order and Inductive Proof | 199 |

Analysis Techniques | 281 |

Elementary Logic | 395 |

Predicate Logic | 457 |

Applied Logic | 517 |

Regular Languages and Finite Automata | 695 |

ContextFree Languages and Pushdown Automata | 759 |

Turing Machines and Equivalent Models | 811 |

Computational Notions | 845 |

Answers to Selected Exercises | 883 |

981 | |

Greek Alphabet | 987 |

995 | |

### Common terms and phrases

A V B algebra algorithm alphabet assume axioms bijection binary relation binary tree Boolean calculus called clausal form clauses closed form closure conjunctive normal form construct contains context-free languages countable defined denote derivation describe deterministic disjunction edge elements equal equation equivalence relation example False Figure finite following wff formal function grammar graph halts inductive definition infinite input string integer left recursion logic program loop means natural numbers nodes nonempty normal form notation obtain the following occur operations pairs polynomial poset predicate premise problem production properties propositional prove quantifiers real number recursive regular expression regular grammar regular languages replace represent sequence Simp solve stack statement subset Suppose surjective symbol tape tautology technique theorem transform transitive true truth table tuples Turing machine valid variables Vx p(x well-founded words write