Lesson 13
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?
These rules state that certain propositions are equivalent to others and therefore may be substituted for them
What is the rules of replacement?
This rule of replacement states the following:
p-=(pvvp), p-=(p*p)
What is the rule of Tautology?
A special rule in a formal proof that allows us to assume the antecedent of a conditional
What is a conditional proof?
Formal proofs can prove validity but not this
What is invalidity?
This rule of replacement states the following:
psupq-=~pvvq
What is the rule of Material Implication/Equivalence?
This rule of replacement states the following:
[(pvvq)vvr-=[pvv(qvvr)]
[(p*q)*r-=[p*(q*r)]
What is the rule of Association?
After assuming the antecedent, we deduce this, then conclude the entire conditional
What is the consequent?
This is a valid argument form which can be used to justify steps in a proof
What is a rule of inference?
This rule of replacement states the following:
a(b+c)=(ab+ac)
What is the rule of Distribution?
This rule of replacement states the following:
psupq-=~qsup~p
What is the rule of Transposition?
To use any part of the conditional proof, you must use this
What is all of it?
It is customary to end proofs with 'Q.E.D.', which stands for this expression in English
What is 'What is to be demonstrated'?
This rule of replacement states that the following are equivalent:
(pvvq), (qvvp)
(p*q),(p*q)
What is the rule of Commutation?
This theorem states that the following are equivalent:
~(p*q), (~pvv~q)
What is De Morgan's Theorem?
A special rule in a formal proof that allows us to assume the negation of a proposition
What is a reductio ad absurdum?
Name as many of the rules of inference as you are able (@100per)
What are modus ponens, modus tollens, hypothetical syllogism, disjunctive syllogism, constructive dilemma, conjunction, absorption, simplification, and addition?
This rule of replacement states the following:
~ ~p-=p
What is the rule of Double Negation?
This rule of replacement states the following:
[(p*q)supr]-=[psup(qsupr)]
What is the rule of Exportation?
After assuming the negation, we deduce this, then conclude the entire proposition
What is a self-contradiction?
These in the rules of inference may, in fact, represent propositions
What are variables?
A set of logical operators is this if and only if all possible combinations of true and false for two variables are derivable using only those logical operators
What is truth-functionally complete?