Vocabulary
A diagram that shows a set of propositions being decomposed into their literals
What is a truth tree?
p ⊃ q
p
therefore q
What is modus ponens?
~(p • q) = (~p v ~q)
~(p v q) = (~p • ~q)
What is De Morgan's Theorem?
A valid argument form which can be used to justify steps in a proof.
What is a rule of inference?
Deny the disjunctive premise and provide a third alternative somewhere in the middle.
What is go between the horns?
A proposition that is broken down into simple propositions
What is decomposed?
p ⊃ q
~q
therefore ~p
What is modus tollens?
p = (q v p)
p = (p • p)
What is a tautology?
The customary way to end a proof
What is Q.E.D.?
Propositions that are true at the same time.
What is consistent?
What are literals?
p
therefore p v q
What is addition?
p = ~~p
What is double negation?
Latin for "what was to be demonstrated".
What is quod erat demonstrandum.
p
q
therefore p • q
What is a conjunction?
A path on a truth tree for which a contradiction has been found.
What is a closed branch?
p v q
~p
therefore q
What is disjunctive syllogism?
(p ⊃ q) = (~p v q)
What is material implication?
A step-by-step deduction of a conclusion from a set of premises, each step being justified by an appropriate basic rule.
What is a formal proof of validity?
Rejecting one of the conditionals in the conjunctive premise.
What is grasp it by the horns?
What is an open branch?
p ⊃ q
q ⊃ r
therefore p ⊃ r
What is hypothetical syllogism?
(p v q) = (q v p)
(p • q) = (q • p)
What is commutation?
A valid argument which presents a choice between two conditionals.
What is a dilemma?
Propositions that cannot all be true.
What is inconsistent?