LPS29 Unit 2 & 3

LOGICALLY EQUIVALENT

if two statement forms truth-values agree for all instances; that is, their truth tables agree in every row

SUBFORMULA

a grammatically correct sentence that is a part of another grammatically correct sentence

PROOF

a sequence of statements, each of which is either a premise or a statement that is obtained from one or more earlier statements by applying one of the rules of inference

an argument is DEDUCTIVELY VALID…

iff it is an instance of a valid form

an argument FORM is DEDUCTIVELY VALID…

iff there are no instances of that form in which all the premises are true and the conclusion false

COMPOUND

iff it logically contains another complete sentence as a component

SIMPLE

iff it is not compound

SENTENTIAL OPERATOR

an expression containing blanks such that, when the blanks are filled with complete sentences, the result is a complete sentence

TRUTH-FUNCTIONAL

iff the truth or falsity of a compound sentence containing that operator is completely determined by the truth or falsity of its component sentences

COUNTEREXAMPLE

an instance of that form where all the premises are true and the conclusion false

TAUTOLOGY

iff every instance of that form is true; that is, it is true in every row in its truth table

CONTRADICTION

iff every instance of that form is false; that is, it is false in every row in its truth table

CONTINGENCY

iff some instance of that form is true and some is false; that is, it is true in at least one row in its truth table and false in at least one row in its truth table