Koofers

Final Exam- Proofs - Flashcards

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Class:PHIL 1504 - Language and Logic
Subject:Philosophy
University:Virginia Polytechnic Institute And State University
Term:Spring 2013
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      Mode:   CARDS LIST       ? pages   PRINT EXIT
Modus Ponens (MP) if p then q
p
__________
q
Disjunctive Syllogism (DS) p or q
~ p
__________
q

*reasoning by elimination
Modus Tollens (MT) if p then q
~q
_________
~p

*if something proves a negative, then it must be wrong
Hypothetical Syllogism (HS) if p then q
if q then r
___________
if p then r

Generated by Koofers.com
Simplifications (Simp) p and q
_______
p

*from a conjunction we can take the first conjuct
Conjunction (Conj) p
q
________
p and q
Constructive Dilemma (CD) p or q
(if p then r) and (if q then s)
______________________
r or s
Addition (Add) p
___________
p or q
Generated by Koofers.com
Commutation (Comm) p or q = q or p

p and q = q and p
Double Negation (DN) p = ~~p

*can't eliminate two ~'s when they are not consecutive- separated by parentheses for example
Transposition (Trans) if p then q = if not q then not p
Material Equivalence (Equiv) if p then if and only if q = (if p then q) and (if q then p)
if p then if and only if q = (p and q) or (not p and not q)
Generated by Koofers.com
Distribution (Dist) p and (q or r) = (p and q) or (p and r)
p or (q and r) = (p or q) and (p or r)
Tautology (Taut) p
_____
p or p

p
_____
p and p
Association (p and q) and r = p and (q and r)
p or (q or r) = (p or q) or r

*connectives must be the same

DeMorgan's Rule (DM) ~ ( p and q ) = (~ p or ~ q )
~ ( p or q ) = (~ p and ~ q )
Generated by Koofers.com
Material Implication (Imp) if p then q = ~ p or q
Exportation (Exp) (if (p and q) then r) = ( if p then (if q then r))

Generated by Koofers.com

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 Modus Ponens (MP)if p then q
p
__________
q
 Disjunctive Syllogism (DS)p or q
~ p
__________
q

*reasoning by elimination
 Modus Tollens (MT)if p then q
~q
_________
~p

*if something proves a negative, then it must be wrong
 Hypothetical Syllogism (HS)if p then q
if q then r
___________
if p then r

 Simplifications (Simp)p and q
_______
p

*from a conjunction we can take the first conjuct
 Conjunction (Conj)p
q
________
p and q
 Constructive Dilemma (CD)p or q
(if p then r) and (if q then s)
______________________
r or s
 Addition (Add)p
___________
p or q
 Commutation (Comm)p or q = q or p

p and q = q and p
 Double Negation (DN)p = ~~p

*can't eliminate two ~'s when they are not consecutive- separated by parentheses for example
 Transposition (Trans)if p then q = if not q then not p
 Material Equivalence (Equiv)if p then if and only if q = (if p then q) and (if q then p)
if p then if and only if q = (p and q) or (not p and not q)
 Distribution (Dist)p and (q or r) = (p and q) or (p and r)
p or (q and r) = (p or q) and (p or r)
 Tautology (Taut)p
_____
p or p

p
_____
p and p
 Association(p and q) and r = p and (q and r)
p or (q or r) = (p or q) or r

*connectives must be the same

 DeMorgan's Rule (DM)~ ( p and q ) = (~ p or ~ q )
~ ( p or q ) = (~ p and ~ q )
 Material Implication (Imp)if p then q = ~ p or q
 Exportation (Exp)(if (p and q) then r) = ( if p then (if q then r))

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