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| Sentential Logic | |
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| Introduction to Logic Why Study Logic? | |
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| What Logic Is All About Induction and Deduction | |
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| Form and Validity Truth and Validity | |
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| The Nature of Symbolic Logic | |
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| The Scope of Symbolic Logic | |
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| Definitions Study | |
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| Questions | |
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| Exercises | |
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| The Structure of Sentential Logic Simple and Compound Sentences Sentential Operators | |
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| The Structure and Symbolism of Sentential Logic | |
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| Definitions Study | |
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| Questions | |
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| Exercises | |
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| Computing Truth Values Truth Tables for the Operators | |
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| Computing Truth Values Truth-functional Operators | |
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| Non-truth-functional Operators | |
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| Definitions Study | |
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| Questions | |
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| Exercises | |
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| Symbolizing English Sentences Simple Sentences Truth-functional and Non-truth-functional | |
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| Compounds Symbolizing Truth-functional | |
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| English Operators Symbolizing Multiply Complex Sentences | |
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| Exercises | |
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| Truth Tables for Testing Validity Constructing Base Columns for Truth Tables | |
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| The Truth Table | |
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| Test for Validity | |
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| Shortcut Validity | |
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| Tests Mechanical Decision Procedures | |
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| Definitions Study | |
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| Questions | |
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| Exercises | |
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| Further Applications of the Truth Table Method Tautologies, Contradictions, and Contingencies | |
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| Logical Implication and Logical | |
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| Equivalence Rules of Inference, Logical Implication, and Logical Equivalence | |
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| Consistency Four Kinds of Truth Table | |
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| Problems and the Relations Between Them | |
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| Definitions Study | |
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| Questions | |
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| Exercises | |
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| The Proof Method: Eight Basic | |
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| Inference Rules Form and Substitution | |
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| Instance The Proof Process Eight Basic | |
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| Inference Rules Derivations and Proofs | |
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| Constructing Simple Proofs | |
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| Constructing More Complex Proofs | |
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| Summary of Rules of Inference | |
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| Definitions | |
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| Exercises | |
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| Replacement Rules | |
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| The Structure of Replacement Rules | |
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| The Ten Replacement Rules Constructing Simple Proofs | |
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| with Replacement Rules Strategies for More Complex Proofs | |
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| Summary of Replacement Rules | |
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| Exercises | |
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| Conditional Proof and Indirect Proof | |
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| Conditional Proof | |
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| Indirect Proof | |
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| Discharging Assumptions; Restrictions on C.P. and I.P. Using C.P. and I.P. Proofs of Theorems Invalidity Truth and Proof | |
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| Summary of Rules of Conditional Proof and Indirect Proof | |
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| Definitions | |
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| Exercises | |
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| Monadic Predicate Logic | |
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| Singular Sentences | |
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| Singular Sentences and Propositional | |
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| Functions Symbolizing Singular Sentences | |
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| Definitions | |
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| Exercises | |
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| Quantifiers Universal and Existential Quantifiers | |
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| Free and Bound Variables; Scope of a Quantifier Negated Quantifiers | |
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| Definitions | |
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| Exercises | |
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| Categorical Propositions | |
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| The Four Categorical Propositions | |
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| Individuals, Sets, and Properties | |
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| Venn Diagrams Symbolizing Categorical Propositions | |
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| Negated Categorical Propositions | |
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| Deriving C.Q.N. Rules from Q.N. Rules Symbolizing English Categorical Sentences | |
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| Summary of Categorical Propositions | |
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| Definitions | |
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| Exercises | |
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| Complex Subjects and Predicates Complex | |
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| Subjects and Predicates Equivalent Symbolizations | |
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| Exercises | |
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| Quantifier Form and Truth-Functional | |
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| Compounds of Quantifier Statements Quantifier | |
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| Form Truth-functional Compounds and Quantifier | |
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| Form Symbolizing Truth-functional Compounds | |
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| Definitions | |
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| Exercises | |
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| Proofs in Predicate Logic Preliminary Statement of the Four Quantifier Rules Instances of Quantified Formulas | |
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| The Rules of Universal Instantiation (U.I.) and Existential Generalization (E.G.) | |
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| The Rules of Existential Instantiation (E.I.) adn Universal Generalization (U.G.) | |
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| Flagging Restrictions Constructing Proofs for "Pure" | |
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| Quantifier Arguments Constructing Proofs for Arguments Containing Truth-functional Compounds | |
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| Constructing Proofs of Quantifier Theorems Statement of the Quantifier Rules, with All Necessary Restrictions | |
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| Exercises | |
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| Invalidity in Quantifier Logic | |
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| The Natural Interpretation Method Truth Conditions for Quantifier Statements | |
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| The Model Universe Method Definitions Exercises | |
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| Relational Predicate Logic | |
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| Symbolization in Relational Predicate Logic | |