Lessons 1-2
A branch of formal logic in which the basic unit of thought is the proposition.
What is propositional logic?
"what was to be demonstrated," used to show a proof is completed
What is Q.E.D. (quod erat demonstrandum)?
A valid argument which presents a choice between 2 conditionals
What is dilemma?
A path on a truth tree which includes no contradictions (mark with an O)
What is open branch?
A statement (a sentence with a truth value).
What is a proposition?
A proposition that is always true due to its logical structure
What is tautology?
Valid argument forms which can be used to justify steps in a proof
What are Rules of Inference?
A path on a truth tree for which a contradiction has been found (mark with row numbers and X)
What is closed branch?
What is a compound proposition?
A proposition that is always false due to its logical structure
What is self-contradiction?
Forms of equivalent statements, which may replace each other wherever they occur (even if part of a larger proposition) and work from left to right AND right to left
What are Rules of Replacement?
A diagram which shows a set of propositions being decomposed into their literals in order to look for contradictions
What is truth tree?
Words which combine or modify simple propositions to make compound propositions
What are logical operators?
A step-by-step deduction of a conclusion from a set of premises, each step being justified by an appropriate basic rule
What is formal proof for validity?
A special rule in a formal proof which allows us to assume the antecedent of a conditional and, once we deduce that consequent, to conclude the entire conditional
What is Conditional Proof?
Break down compound propositions into simple propositions (or their negation), which are called literals
What is decompose?
A list of the possible truth values for a set of one or more propositions
What is truth table?
A set of propositions that can all be true at the same time.
What is consistent propositions?
A special rule in a formal proof which allows us to assume the negation of a proposition, deduce a self-contradiction, then conclude the original proposition.
What is Reductio ad Absurdum?
Simple propositions or negations of simple propositions
What are literals?