274-6.PL-Translation_TruthTables-1 (1)

Propositional Logic (PL)

A symbolic language that has more in common with computer programming languages, representing simple propositions and Boolean operations.

Boolean Operators

Functions in propositional logic that include conjunction (•), disjunction (Ú), conditional (É), biconditional (≡), and negation (~).

Tautologous Statement

A statement that is always true regardless of the truth values of its components.

Contingent Statement

A statement whose truth value varies depending on the truth values of its components.

Self-Contradictory Statement

A statement that is always false, with no case in which it is true.

Logical Equivalence

Two propositions that hold the same truth value in all possible cases.

Indirect Truth Table

A method for evaluating the validity of arguments by assuming the premises are true and deriving the truth values of components.

Consistency in Propositions

A set of statements that can all be true at the same time, with no contradictions present.

Main Operator

The operator in a compound statement that combines or operates over its largest component statements.

Truth Value

The designation of a statement as either true (T) or false (F) in propositional logic.

Truth Table

A table used to compute the truth value of propositions based on their components and logical operators.

Negation (~)

An operator that indicates that a statement is 'not true' or negates the truth value of its following statement.

Conjunction (•)

A binary operator that combines two statements and is true if both statements are true.

Disjunction (Ú)

A binary operator that combines two statements and is true if at least one of the statements is true.

Conditional (É)

An operator that indicates that if one statement is true, then another statement must also be true.

Biconditional (≡)

An operator that indicates that two statements are equivalent or have the same truth value.