6.2 Truth Functions
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6.2 Truth Functions

Course Number: PHIL 110, Fall 2008

College/University: South Carolina

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Propositional Logic Truth Functions Introduction In 6.1 we symbolized simple statements and applied operators to natural language in order to show the logical form of statements. In this section we will learn how to assess the truth of logical forms by defining the operators that compose them. Last, we will reveal various problems with our symbolic language in capturing the meaning of natural language....

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Logic Truth Propositional Functions Introduction In 6.1 we symbolized simple statements and applied operators to natural language in order to show the logical form of statements. In this section we will learn how to assess the truth of logical forms by defining the operators that compose them. Last, we will reveal various problems with our symbolic language in capturing the meaning of natural language. Truth-Functional Definitions of the Logical Operators Logical operators are functional in that the truth value of a compound proposition is determined by the truth value of its components in relation to the definition of the operator. The definitions of the logical operators are presented in terms of statement variables, such as the lower-case letters p, q, r, and s. These variables stand for any possible statement, say A or (A B). Statement Forms Statement variables are used to construct statement forms, which is an arrangement of statement variables and operators such that the uniform substitution of the statements in place of the variables results in a statement. The statement form is determined by the main operator. The main operator is the operator that controls the whole sentence. The following are instances of statement variables being substituted by statements keeping the statement form. Negations Below is the statement form " q". Remember q is a variable. The statements under q are substitution of instances the statement form. Notice, all of the statements are negations. Conjunctions Disjunctions Conditionals Biconditionals Truth-Functional Definitions of Boolean Operators We will give definitions to each of our Boolean connectives in the following slides. These are functional definitions in that the definition of the operator depends on the definition of the constituent statements. So, we will define our operators with the truth table method. A truth table is an arrangement of truth values that shows in every possible case how the truth value of a compound proposition is determined by the truth values of its simple components. The Truth-Functional Definition of "not" Statements The Truth-Functional Definition of "and" Statements The Truth-Functional Definition of "or" Statements The Truth-Functional Definition of "If...then..." Statements The Truth-Functional Definition of "if and only if" Statements Try This One! Determine truth values of the following statement. Let A and B be true and M be false. Register to View Answer Try Another Determine whether the following compound statement is true or false. A and B is true, while M and N is false. Register to View Answer Problems with Symbolic Translations There are various cases in which our symbolic language does not fully capture the meaning of statements in colloquial English. For examples of these see p. 297299.

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South Carolina - PHIL - 110
South Carolina - PHIL - 110
1 The following are some answers to various problems in section 6.1.2
South Carolina - PHIL - 110
1CRUISE'S CROP CIRCLES"A Proof from a Small Silver Saucer""Cruise's Crop Circles" is two proofs that can be completed in order to achieve a 100 on Test #2. If you can complete the following problems before Test #2 and can explain them to me during my o
South Carolina - PHIL - 110
Validity an argument is valid when the conclusion cannot be false given that the premises are true. That is, if you assume the premises are true and the conclusion is necessarily entailed by the premises, then the argument is valid. NOTE: VALIDITY HAS NOT
South Carolina - PHIL - 110
South Carolina - PHIL - 110
The following are problems from 7.1 and 7.2. Each problem has either the justification or the derivation completed. You are to complete the underlined portion. This should help you in completing proofs. For additional problems like these, see 7.1 sections
South Carolina - PHIL - 110
The Logic Twelve-Step ProgramA Program for Those Troubled with Deductive LogicI. Introduction The PHIL 110 (Deductive Logic) Twelve-Step Program is designed for those students that are having serious problems with symbolic logic. I have received a numbe
South Carolina - PHIL - 110
South Carolina - FINA - 363
Capital BudgetingReading: Text Chapters 13 and 12 (disregard MCC stuff in 12)Some Recent Examples I02 April 2002: "On Monday evening, Hyundai announced its decision to locate the company's first American auto plant in Montgomery. The facility, which is
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Capital Structure DecisionsReadings: Text Chapter 13OverviewAssets Current Assets Cash Receivables Inventories Other Long-Term Assets PPE Net Notes Rec.Affl. Joint Ventures Goodwill Reaq.Franchises Other 21,029 68,666 28,864 20,085 138,644 284,716 7,60
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Derivative SecuritiesReadings: Online Chapter on Derivatives2/14/11Finance 363: Lecture 111What is a Derivative?Characteristics of Derivatives:Financial security whose value is a function of "price" of some underlying asset, but which does not repr
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The Mathematics of FinanceReadings: Text Chapter 9. OVERVIEW Present Value and Future Value of a Single Cash Flow. Present Value and Future Value of Multiple Cash Flows. Conventions for Reporting Interest Rates. Using Your Financial Calculator.1Why "
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Solving For k Or nExample: Assume you have $1,200 to invest and want to know how long it will take for that sum to grow to $3,000 if invested in a CD at 7%:1Solving For k Or nExample: Assume you have $1,200 to invest and want to know how long it will
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More Complex ExampleStarting next year, you plan on investing $3,000 per year for 15 years. At year 16, you will begin investing $5,000 per year for an additional 15 years. If your investments return 11% per year, how much will you have on the date of yo
South Carolina - FINA - 363
Risk and ReturnReading: Text Ch. 11Determination of "k" Fact: All investors are naturally risk averse somemore than others. Implication: In equilibrium, more risky assets mustoffer investors a higher expected rate of return or else no one will purch
South Carolina - FINA - 363
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South Carolina - FINA - 363
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South Carolina - FINA - 363
Asset Valuation: EquityReadings: Text Ch. 10Valuing Equity: ComplicationsDifficulties in valuing equity/common stock: 1. Residual claimant on firm value. 2. Each firm is unique. 3. Usually only one class of common per firm. Assumptions for the moment
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South Carolina - MGSC - 395
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South Carolina - MGSC - 395
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"The Goal" Discussion Questions 1. What kind of problems did the Bearington Plant face before Alex Rogo met with Jonah at the Chicago Airport? 2. What three measurements of productivity did Jonah apply to Alex's situation?3. What were the lessons of bott
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