Ra101 exam 1

Biconditional

A compound statement made up of two conditionals—one indicated by the word "if" and the other indicated by the phrase "only if."

What is a Conjunction?

A compound statement that has two distinct statements (called conjuncts) connected by the dot symbol.

What is a Disjunction?

A compound statement that has two distinct statements (called disjuncts) connected by the wedge symbol.

Argument

A group of statements in which the conclusion is claimed to follow from the premise(s)- Arguments can have more than one premise but only one conclusion

Inferential claim

A passage makes an inferential claim when it expresses a reasoning process

Statement

A sentence that is either true or false

Compound statement

A statement that has at least one simple statement and at least one logical operator as components.

Self-contradiction

A statement that is necessarily false.

Tautology

A statement that is necessarily true.

Substitution instance

A substitution instance of a statement occurs when a uniform substitution of statements for the variables results in a statement. A substitution instance of an argument occurs when a uniform substitution of statements for the variables results in an argument.

Modus ponens

A valid argument form (also referred to as affirming the antecedent).

Modus tollens

A valid argument form (also referred to as denying the consequent).

Truth table

An arrangement of truth values for a truth-functional compound proposition that displays for every possible case how the truth value of the proposition is determined by the truth values of its simple components.

Fallacy of affirming the consequent

An invalid argument form; it is a formal fallacy.

Fallacy of denying the antecedent

An invalid argument form; it is a formal fallacy.

Well-formed formula

Any statement letter standing alone, or a compound statement such that an arrangement of operator symbols and statement letters results in a grammatically correct symbolic expression.

Truth value

Every statement has a truth value (either true or false)

What is a Conditional statement:?

In ordinary language, the word "if" typically precedes the antecedent of a conditional statement, and the statement that follows the word "then" is referred to as the consequent.

Argument form

In propositional logic, an argument form is an arrangement of logical operators and statement variables such that a uniform substitution of statements for the variables results in an argument.

Statement form

In propositional logic, an arrangement of logical operators and statement variables such that a uniform substitution of statements for the variables results in a statement.

Simple statement

One that does not have any other statement or logical operator as a component.

Logical operators

Special symbols that are used to translate ordinary language statements. • The basic components in propositional logic are statements.

Noncontingent statements

Statements such that the truth values in the main operator column do not depend on the truth values of the component parts.

Contingent statements

Statements that are neither necessarily true nor necessarily false (they are sometimes true, sometimes false).

Proposition

The information content or meaning of a statement.

Main operator

The operator that has the entire well-formed formula in its scope.

Order of operations

The order of handling the logical operators within a truth-functional proposition; it is a step-by-step method of generating a complete truth table.

Scope

The statement or statements that a logical operator governs.

Truth-functional proposition

The truth value of any compound proposition using one or more of the five operators is a function of (that is, uniquely determined by) the truth values of its component propositions.

Inconsistent statements

Two (or more) statements that do not have even one line on their respective truth tables where the main operators are true (but they can be false) at the same time.

Consistent statements

Two (or more) statements that have at least one line on their respective truth tables where the main operators are true.

Contradictory statements

Two statements that have opposite truth values under the main operator on every line of their respective truth tables.

Logically equivalent statements

Two truth-functional statements that have identical truth tables under the main operator.

What is a Inclusive disjunction?

When we assert that at least one disjunct is true, and possibly both disjuncts are true. Given this, an inclusive disjunction is false when both disjuncts are false, otherwise it is true.

What is a Exclusive disjunction?

When we assert that at least one disjunct is true, but not both. In other words, we assert that the truth of one excludes the truth of the other. Given this, an exclusive disjunction is true when only one of the disjuncts is true, otherwise it is false.

Sufficient condition

Whenever one event ensures that another event is realized.

Necessary condition

Whenever one thing is essential, mandatory, or required in order for another thing to be realized.

Logic

the systematic use of methods and principles to analyze, evaluate, and construct arguments