First Course in Mathematical Logic

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Overview


Starting with symbolizing sentences and sentential connectives, this work proceeds to the rules of logical inference and sentential derivation, examines the concepts of truth and validity, and presents a series of truth tables. Subsequent topics include terms, predicates, and universal quantifiers; universal specification and laws of identity; axioms for addition; and universal generalization. 1964 edition. Index.
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First Course in Mathematical Logic

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Overview


Starting with symbolizing sentences and sentential connectives, this work proceeds to the rules of logical inference and sentential derivation, examines the concepts of truth and validity, and presents a series of truth tables. Subsequent topics include terms, predicates, and universal quantifiers; universal specification and laws of identity; axioms for addition; and universal generalization. 1964 edition. Index.
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Editorial Reviews

From The Critics
Some 40 years after its original publication (Blaisdell Publishing Co., 1964), this reprint makes available Suppes' and Hill's (both, Stanford U.) text, which aims to provide an accessible and clear presentation of mathematical logic for high school and elementary college mathematics classrooms. Coverage includes the sentential theory of inference, inference with universal quantifiers, and applications of the theory of inference developed to the elementary theory of communicative groups. Annotation c. Book News, Inc., Portland, OR
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Product Details

  • ISBN-13: 9780486422596
  • Publisher: Dover Publications
  • Publication date: 6/17/2010
  • Series: Dover Books on Mathematics Series
  • Edition description: Reprint
  • Pages: 288
  • Sales rank: 637,310
  • Product dimensions: 5.40 (w) x 8.40 (h) x 0.60 (d)

Table of Contents

1. Symbolizing Sentences
  1.1 Sentences
  1.2 Sentential Connectives
  1.3 The Form of Molecular Sentences
  1.4 Symbolizing Sentences
  1.5 The Sentential Connectives and Their Symbols--Or; Not; If . . . then . . .
  1.6 Grouping and Parentheses. The Negation of a Molecular Sentence
  1.7 Elimination of Some Parentheses
  1.8 Summary
2. Logical Inference
  2.1 Introduction
  2.2 Rules of Inference and Proof
    Modus Ponendo Ponens
    Proofs
    Two-Step Proofs
    Double Negation
    Modus Tollendo Tollens
    More on Negation
    Adjunction and Simplification
    Disjunctions as Premises
    Modus Tollendo Ponens
  2.3 Sentential Derivation
  2.4 More About Parentheses
  2.5 Further Rules of Inference
    Law of Addition
    Law of Hypothetica Syllogism
    Law of Disjunctive Syllogism
    Law of Disjunctive Simplification
    Commutative Laws
    De Morgan's Laws
  2.6 Biconditional Sentences
  2.7 Summary of Rules of Inference. Table of Rules of Inference
3. Truth and Validity
  3.1 Introduction
  3.2 Truth Value and Truth-Functional Connectives
    Conjunction
    Negation
    Disjunction
    Conditional Sentences
    Equivalence: Biconditional Sentences
  3.3 Diagrams of Truth Value
  3.4 Invalid Conclusions
  3.5 Conditional Proof
  3.6 Consistency
  3.7 Indirect Proof
  3.8Summary
4. Truth Tables
  4.1 Truth Tables
  4.2 Tautologies
  4.3 Tautological Implication and Tautological Equivalence
  4.4 Summary
5. Terms, Predicates, and Universal Quantifiers
  5.1 Introduction
  5.2 Terms
  5.3 Predicates
  5.4 Common Nouns as Predicates
  5.5 Atomic Formulas and Variables
  5.6 Universal Quantifiers
  5.7 Two Standard Forms
6. Universal Specification and Laws of Identity
  6.1 One Quantifier
  6.2 Two or More Quantifiers
  6.3 Logic of Identity
  6.4 Truths of Logic
7. A Simple Mathematical System: Axioms for Addition
  7.1 Commutative Axiom
  7.2 Associative Axiom
  7.3 Axiom for Zero
  7.4 Axiom for Negative Numbers
8. Universal Generalization
  8.1 Theorems with Variables
  8.2 Theorems with Universal Quantifiers
Index
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