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42 Cards in this Set

  • Front
  • Back
p C q
p
____
q
modus Poenens (MP)
p C q
~q
_______
~p
Modus Tollens (MT)
p C q
q C r
_______
p C r
Hypothetical Syllogism
p v q
~p
_____
q
Disjunctive Syllogism
(p C q).(r C s)
p V r
_____
q v s
Constructive Dilemma
p . q
________
p
Simplification
p
q
__
p.q
Conjunction
p
___
p v q
Addition
~(p . q )= (~p v ~q)
~ ( p v q)= (~p.~q)
DeMorgan's Theorem
(pvq)= (qvp)
p.q = q.p
Commutation
[(pvq)vr]=[p v (q v r )]
[p .(q .r)]= [(p.q).r]
Association
[p.(qvr)]= [(p.q)v (p.r)]
[p v(q.r)]= [(pvq).(pvr)]
Distribution
p=~~p
Double Negation
(pCq)=(~pvq)
Material Implication
(pcq)=(~qc~p)
Transposition
(p=q)=[(pcq).(qcp)]
(p=q)= [(p.q)v (~p . ~q)]
Material Equivalence
[(p.q)c r]= [(pc (q c r)]
Exportation
p=(pvp)
p=(p.p)
Tautology
What does Modus Ponens allow us to do?
assert the consequent of a conditional statement on a line by itself
What does Modus Tollens allow us to do?
allows us to assert the negation of the antecendent
What does Hypothetical syllogism allow us to do?
used to derive a conditional statement from two other conditionals
what does Disjunctive Syllogism allow us to do?
allows us to assert the righ-hand disjunct of a disjunctive statement on a line by itself
What does Constructive Dilemma allow us to do?
it's two modus ponens steps from (p c q) and (r c s) and p v r to infer q v s
What does Simplification allow us to do?
from p.q infer p . Reverse of conjunction statement is true, then each of its atomic statements is true. 2 propositions are given as ture on a single line, then each of them is true separately
What does a conjunction allow us to do?
two propositions asserted separately on different lines may be conjoined on a single line
What does addition allow us to do?
whenever a proposition is asserted on a line by itself it may be joined disjunctively w/any other proposition we choose. From p to infer pvq fir a disjunction to be true, only one of them needs to be true
What does DeMorgan's Theorem allow us to do?
only for conjunctive and disjunctive statements. When moving a tilde inside or outside a set of parentheses, a dot switches with a wedge and vice versa
What does Commutation allow us to do?
asserts the truth value of a conjunction or disjunction is unaffected by the order in which the components are listed. The statement may be commuted or switched fro one another w/0 affecting the truth value
What does Association allow?
states that the truth value of a conjunction or disjunctive statement is unaffected by the placement of ()when the same operator is used throughout
What does distribution allow?
applies only to conjunctive and disjunctive statements. When a proposition is conjoined to a disjunctive statement in () or disjoined to a conjunctive statement in () the rule allows us to put the proposition together w/each of the components inside the () and go in the reverse direction
What does double negation allow?
pairs of tildes immediately adjacent to one another may be either deleted or introduced w/o affecting the truth value
What does Material Implication allow?
substitute actual statements in place of letters; states that a horseshoe may be replaced by a wedge if the left-hand component is negated, and the reverse replacement is allowed if a tilde is deleted from the left-hand component
What does Transposition allow?
the antecendent and consequent may swith places if and only if both are negated
What does Material Equivalence allow?
either p and q are both true or p and q are both false
what does exportation allow?
if we have p then if we have r is logically equivalent to if we have both p and q we have r
What does tautology allow?
to eliminate the redundancy in disjunctions and conjunctions
What does double negation allow?
pairs of tildes immediately adjacent to one another may be either deleted or introduced w/o affecting the truth value
What does Material Implication allow?
substitute actual statements in place of letters; states that a horseshoe may be replaced by a wedge if the left-hand component is negated, and the reverse replacement is allowed if a tilde is deleted from the left-hand component
What does Transposition allow?
the antecendent and consequent may swith places if and only if both are negated
What does Material Equivalence allow?
either p and q are both true or p and q are both false
what does exportation allow?
if we have p then if we have r is logically equivalent to if we have both p and q we have r
What does tautology allow?
to eliminate the redundancy in disjunctions and conjunctions