Symbols and Operators
A logical operator that is only true with both propositions are true
What is a conjunction?
This is another word for a proposition.
What is a statement?
This is a proposition that is always true due to its logical structure.
What is a tautology?
A path on a truth tree which includes no contradictions.
What is an Open Branch?
This is the symbol for a conjunction
What is the dot?
A logical operator that is true when at least one of the propositions is true
What is a disjunction?
This is the definition for logic as presented by James B. Nance?
What is The science of Art and Reasoning?
A valid argument form which can be used to justify steps in a proof.
What are the rules of inference?
A path on a truth tree for which a contradiction has been found.
What is a closed branch?
A listing of the possible truth values for a set of one or more propositions.
What is a Truth Table?
A logical operator that is true with both propositions are the same
What is a biconditional?
This represents a single proposition and is typically symbolized with a capital letter
What is a propositional constant?
Forms of equivalent statements.
What are the rules of replacement?
A diagram that shows a set of propositions being decomposed into their literals.
What is a Truth Tree?
a valid argument which presents a choice between two conditionals.
What is a Dilemma?
This symbol negates a given proposition
What is the tilde?
What is a propositional variable?
A proposition is _____ __________ when its truth depends upon the truth values of its component parts.
What is truth functional?
A special rule which allows us to assume the negation of a proposition, deduce a self-contradiction, then conclude the proposition.
What is Reductio ad Absurdum?
The rule of Inference:
If p then q
p
therefore q
What is Modus Ponens?
A logical operator that is only false when the antecedent is true and the conclusion is false
What is a conditional (hypothetical)?
The biconditional can be placed between two propositions in order to check for these three things
What are Logical Equivalence, non-equivalence, and contradiction?
A way of deducing a conclusion from a given set of premises in a series of steps.
What is a formal proof of validity?
A special rule in a formal proof which allows us to assume the antecedent of a conditional and, once we deduce the consequent, conclude the entire conclusion.
What is the Conditional Proof?
a Truth Table with two variables needs this many rows.
What is four?