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Intermediate Logic Classical Conversations


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Propositional Logic
A branch of formal, deductive Logic in which the basic unit of thought is the proposition
Truth-functional
A proposition is_____ when it’s truth value depends upon the truth values of its component parts
Simple Proposition
A proposition with only one component part
Compound Proposition
A proposition with more than one component part ( or modified in another way)
Logical Operators
Words that combine or modify simple propositions to make compound proportions
Proportional Constant
An uppercase letter that represents a single, given proposition
Propositional Variable
A lowercase letter that represents any proposition
Negation
The logical operator that denies or contradicts a proposition
Truth Table
A listing of the possible truth values for a set of one or more propositions
Defining Truth Table
A____ displays the truth values produced by a logical operator modifying a minimum number of variables
Conjunction
A logical operator that joins two propositions and is true if and only if both the propositions are true
Disjunction
A logical operator that joins two propositions and is true if and only if one or both of the propositions is true
Conditional
The_______ operator asserts that one component implies the other. It is false if and only if the antecedent is true and the consequent is false
Antecedent
The proposition following the “if”
Consequent
The proposition following the “then”
Logically Equivalent
Two propositions are______ if and only if they have identical truth values in a truth table
Tautology
A proposition that is always true due to its logical structure
Self-contradiction
A proposition that is false by logical structure
Valid Argument
In a_____, if the premises are true, the conclusion must be true
Invalid Argument
If the premises can be true and the conclusion false, it is a_______
Consistent
When propositions can be true at the same time
Dilemma
A valid argument which presents a choice between two conditionals
Constructive Dilemma
________ work like modus ponens
Destructive Dilemma
_______work like modus tollens
Formal Proofs of Validity
A step-by-step deduction of a conclusion from a set of premises, each step being justified by an appropriate basic rule
Rules of Inference
Valid argument forms which can be used to justify steps in proof
De Morgan’s Theorems
(~p v q) = (p•q)
Commutation
(p v q) = (q v p)
Association
[(p v q) v r) = [p v (q v r)] and [(p•q)•r]=[p•(q•r)]
Distribution
[p• (q v r)]= [(p•q) v (p•r)] and [p v (q•r)]=[(p v q) • (p v r)]
Double Negation
~~p = p
Transposition
( if p then q) = ( if ~q then ~p)
Material Implication
( if p then q) = (~p v q)
Material Equivalence
[(p=q) = (if p then q) • (if q then p)]
Exportation
[if (p•q) then r] = [ if p then (if q then r)]
Tautology
p = (p v p) and p = (p•p)
Conditional Proof
A special rule in a formal proof which allows us to assume the antecedent of a conditional and, once we delude the consequent, to conclude the entire conditional
Reductio and Absurdum
A special rule which allows us to assume the negation of a proposition, device a self-contradiction, then conclude the proposition
NOR
The logical operator_________ is equivalent to ~(p v q). It is truth-functionally complete
Truth-functionally Complete
A set of logical operators is________ if and only if all possible combinations of true and false for two variables are derivable using only those logical operators
Truth Tree
A diagram that shows a set of propositions being decomposed into their literals
Recover the Truth Values
Determining the truth values of the simple propositions for which the propositions in the set would all be true
Open Branch
A path on a truth tree which includes no contradictions
Closed Branch
A path on a truth tree for which a contradiction has been found
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