Southeast Missouri State University



Symbolic Logic I Final Exam Study Guide

For the final exam you should:

(1) Be able to define deductive validity, soundness, and consistency.

(2) Be able to explain why a deductively valid argument with a false conclusion must have at least one false premise. Give an example of a deductively valid argument with a false conclusion.

(3) Be able to add parentheses as needed to a formulae so as to make it a WFF with a specified structure.

(4) Be able to determine the truth value of a compound statement based on a specified interpretation of the truth values of the simple statements occurring in it.

(5) Be able to symbolize complex sentences utilizing parentheses and brackets and the symbols for conjunction, negation, implication, and disjunction.

(6) Be able to construct truth-tables for symbolic formulas.

(7) Be able to use truth-tables to demonstrate the non-validity of argument forms.

(8) Be able to use truth-tables to demonstrate the validity of argument forms.

(9) Be able to use truth-tables to demonstrate the truth of replacement rules.

(10) Be able to symbolize arguments and test for validity using a truth table.

(11) Be able to apply the transformation rules DeMorgan, distribution, implication, transposition, and exportation to formulae as directed.

(12) Be able to apply the inference rules modus ponens, modus tollens, disjunctive syllogism, hypothetical syllogism, and constructive dilemma to formulae.

(13) Be able to construct deductive proofs for symbolized arguments.

(14) Be able to transcribe English statements and arguments into proper symbolic notation, utilizing parentheses and brackets and the symbols for conjunction, negation, implication, and disjunction, and to identify the premises and conclusion of the arguments.

(15) Be able to construct deductive proofs for arguments that you have symbolized.

(16) Be able to utilize abbreviated truth table tests as a means of verifying your symbolization of an argument and to explain the usefulness of this method of testing symbolization.

(17) Be able to utilize an abbreviated truth table in testing an argument for validity or non-validity.

(18) Be able to describe the procedure used in an indirect proof and explain why that procedure is legitimate.

(19) Be able to describe the procedure used in a conditional proof and explain why that procedure is legitimate.

(20) Be able to construct Venn diagrams for each of the four types of categorical propositions and to state whether a given proposition is an A, E, I, or O.

(21) Be able to discuss the logical relations Aristotle organizes on the square of opposition (contrary, sub-contrary, contradictory, sub-altern).

(22) Be able to state the logical relation that obtains between the members of a pair of categorical propositions.

(23) Construct a Venn diagram test for validity for a categorical syllogism.

(24) Be able to apply the four rules for syllogistic validity to a categorical syllogism. This requires an understanding of the concepts of quantity, quality, and the distribution of terms in a categorical proposition.

(25) Be able to define the terms "quantifier" (both existential and universal), "predicate" (both monadic and polyadic or relational) and "individual variable" as used in predicate logic, including the difference between a free variable, a bound variable, and an individual constant.

(26) Be able to explain the conceptual advantage that predicate logic has, as a tool for analyzing arguments, over both sentential logic and syllogistic logic.

(27) Be able to transcribe English sentences into proper symbolic notation using the machinery of quantifiers (both existential and universal), predicates (both monadic and relational), and individual constants.

(28) Be able to construct a truth-functional expansion of a quantified formula across a finite universe of discourse and to state whether a given formula is true or false for a finite universe depending on an interpretation of the extension of the predicates provided for you.

(29) Be able to state precisely the position of the mechanical jurist (paying particular attention to the relation between logic and legal reasoning) and to state the connection between the mechanical jurists view of legal validity and standard concepts of deductive validity.

(30) Be able to articulate some of the reasons that motivate people to adopt the view of the mechanical jurist.

(31) Be able to give examples, citing cases, of problems with the mechanical jurist's view of legal reasoning, paying attention to the nature of the problem that the case presents.

(32) Be able to discuss some of the difficulties associated with rejecting the mechanical jurist's view of legal reasoning.

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