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A Concise Introduction to Logic: Chapter 6 Propositional Logic flashcards |
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• ### Operators (Connectives)

Symbols used to connect simple propositions in propositional logic (pg. 316).

### Propositional Logic

A kind of logic in which the fundamental components are whole statements or propositions (pg. 316).

### Simple Statement

A statement that does not contain any other statement as a component (pg. 317).

### Compound Statement

A statement that contains at least one simple statement as a component (pg. 317).

### Negation

A statement having a tilde as its main operator (pg. 318).

### Conjunctive Statement (Conjunction)

A statement having a dot as its main operator (pg. 318).

### Disjunctive Statement (Disjunction)

A statement having a wedge as its main operator (pg. 318).

### Conjuncts

A component in a conjunctive statement on either side of the main operator (pg. 318).

### Disjuncts

The component in a disjunctive statement on either side of the main operator (pg. 318).

### Conditional Statement (Conditional)

(1) An "if...then" statement (2) a statement having a horseshoe as its main operator (pg. 318).

### Material Implication

The relation expressed by a truth-functional biconditional (pg. 318).

### Antecedent

(1) The component of a conditional statement immediately following the word "if" (2) the component of a conditional statement to the left of the horse-shoe (pg. 318).

### Consequent

(1) The component of a conditional statement immediately following the word "then"; the component of a conditional statement that is not the antecedent (2) the component of a conditional statement to the right of the horseshoe (pg. 318).

### Biconditional Statement (Biconditional)

A statement having a triple bar as its main operator (pg. 318).

### Material Equivalence

The relation expressed by a truth-functional biconditional (pg. 318).

### Main Operator

The operator (connective) in a compound statement that has its scope everything else in the statement (pg. 319).

### Sufficient Condition

The condition represented by the antecedent in a conditional statement (pg. 321).

### Necessary Condition

The condition represented by the consequent in a conditional statement (pg. 321).

### Well-Formed Formulas (WFFs)

A syntactically correct arrangement of symbols (pg. 325).

### Truth Functions

A compound proposition whose truth value is completely determined by the truth values of its components (pg. 330).

### Statement Variables

A lowercase letter, such as p or q, that can represent any statement (pg. 330).

### Statement Form

An arrangement of statement variables and operators such that the uniform substitution of statements in place of the variables results in a statement (pg. 330).

### Truth Table

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 (pg. 330).

### Logically True

A statement that is necessarily true; a tautology (pg. 345).

### Logically False

A statement that is necessarily false; a self-contradictory statement (pg. 345).

### Contingent Statement

A statement that is neither necessarily true nor necessarily false (pg. 345).

### Logically Equivalent Statements

(1) statements that necessarily have the same truth value (2) statements having the same truth value on each line under their main operators (pg. 346).

Statements that necessarily have opposite truth values (pg. 346).

### Consistent Statements

Statements for which there is at least one line on their truth tables in which all of them are true (pg. 346).

### Inconsistent Statements

Statements that there is no line on their truth tables in which all of them are true (pg. 346).

### Corresponding Conditional

The conditional statement having the conjunction of an argument's premises as its antecedent and the conclusion as its consequent (pg. 354).

### Argument Form

(1) An arrangement of words and letters such that the uniform substitution of terms or statements in place of the letters results in an argument (2) an arrangement of statement variables and operators such that the uniform substitution of statements in place of the variables results in an argument (pg. 368).

### Substitution Instance

An argument or statement that has the same form as a given argument form or statement (pg. 368).

### Disjunctive Syllogism

(1) A syllogisms having a disjunctive statement for one or both of its premises (2) a valid argument form/rule of inference (pg. 368).

### Pure Hypothetical Syllogism

A valid argument form/rule of inference: "If p then q / If q then r // If p then r" (pg. 369).

### Modus Ponens ("Asserting Mode")

A valid argument form/rule of inference: "If p then q / p // q" (pg. 370).

### Modus Tollens ("Denying Mode")

A valid argument form/ rule of inference: "If p then q / not q // not p" (pg. 370).

### Affirming the Consequent

An invalid argument form: "If p then q / q // p" (pg. 370).

### Denying the Antecedent

An invalid argument form: "If p then q / not p // not q" (pg. 370).

### Constructive Dilemma

A valid argument form/rule of inference "If p then q, and if r then s/ p or r // q or s" (pg. 371).

### Destructive Dilemma

A valid argument form/rule of inference: "If p then q, and if r then s/ not q or not s // not p or not r" (pg. 371).

Example: