Avsnitt
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Information on the class -- grading, sections, homework; and an introduction to what logic is, and how we will be approaching it in this class.
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Information on the class -- grading, sections, homework; and an introduction to what logic is, and how we will be approaching it in this class.
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Saknas det avsnitt?
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Here we begin describing the formal structures underlying reasoning - arguments, statements, and the recursive nature of statement operators.
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Here we begin describing the formal structures underlying reasoning - arguments, statements, and the recursive nature of statement operators.
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Translating natural language into the formal notation of sentential logic, including necessary & sufficient conditions, and recursively structured compound statements.
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Translating natural language into the formal notation of sentential logic, including necessary & sufficient conditions, and recursively structured compound statements.
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Discussion of functions, truth functions, the truth functions symbolized by statement operators, and the construction of truth tables to evaluate compound expressions.
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Discussion of functions, truth functions, the truth functions symbolized by statement operators, and the construction of truth tables to evaluate compound expressions.
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Using truth tables to assess relations of equivalence, consistency and implication among sets of statements; and assessing argument validity.
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Using truth tables to assess relations of equivalence, consistency and implication among sets of statements; and assessing argument validity.
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An introduction to the proof method in sentential logic, with examples using five inference rules (MP, MT, DS, HS, simp).
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An introduction to the proof method in sentential logic, with examples using five inference rules (MP, MT, DS, HS, simp).
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Additional inference rules (dil, DI, conj), and three replacement rules (CE, DN, comm). Examples of more complicated proofs.
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Additional inference rules (dil, DI, conj), and three replacement rules (CE, DN, comm). Examples of more complicated proofs.
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Introduction of final seven replacement rules (DeM, BE, contra, dist, exp, assoc, dup); and introduction to the method of indirect proof.
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Introduction of final seven replacement rules (DeM, BE, contra, dist, exp, assoc, dup); and introduction to the method of indirect proof.
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Introduction to conditional proof; multiple and nested subproofs; using the proof method to verify that a statement is a tautology.
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Introduction to conditional proof; multiple and nested subproofs; using the proof method to verify that a statement is a tautology.
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Clarification of issues that often cause problems, including: negation, the interpretation of statement variables and operator specificity in rule schematics, and requirements on subproofs.
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Clarification of issues that often cause problems, including: negation, the interpretation of statement variables and operator specificity in rule schematics, and requirements on subproofs.
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