Propositional Logic Flashcards
Well-formed formulas
Compound statement forms that are grammatically correct
Propositional logic
Basic components are statements
Inclusive disjunction
Both disjuncts can be true at the same time
Exclusive disjunction
Both disjuncts cannot be true at the same time
Contingent statements
Statements that are neither necessarily true nor necessarily false
Non contingent statements
Statements such that the truth values in the main operator column do not depend on the truth values of the component parts
Tautology
Statement that is necessarily true- empty truth- I will join you OR I will not join you
Self-contradiction
Statement that is necessarily false- I will join you AND I will not join you
Logically equivalent
2 truth-functional statements may appear but have identical truth tables
Contradictory statements
2 statements that have opposite truth values on every line of their respective truth tables
Consistent statements
2 or more statements that have at least one line on their respective truth tables where the main operators are true
Inconsistent statements
2 or more statements that do not have even one line on their respective truth tables where the main operators are true at the same time
Invalid argument
T/T//F
Valid argument
Any table that does not have a line of T/T//F
Technical validity
When the conclusion of an argument is a tautology or when at least one of the premises is a self contradiction. Not sound
