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 Posted: Mon Oct 17, 2005 10:07 am
Using the laws I'll list in Post 2, can you solve the prblem posed above you? Can you pose a new one? Please know how to solve any problem you pose.
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Posted: Mon Oct 17, 2005 10:43 am
Legand:
> is If then (example P>Q is If P then Q)
& is Therefore
* is And
v is Or
~ is not
+ is juxtaposable with
= is If and ony if
Leval 1
Modus Ponens (MP):
P >Q
P
-----
& Q
Modus Tollens (MT):
P>Q
~Q
------
&~P
Hypothetical Syllogism (HS):
P>Q
Q>R
------
&P>R
Disjunctive Syllogism (DS):
PvQ
~P
-----
&Q
Constructive Dilemma (CD):
(P>Q) * (R>S)
PvR
-----
&QvS
Absorption (abs):
P>Q
----
& P>(P*Q)
Simplification (Simp.):
P*Q
----
& P
Conjunction (conj.):
P
Q
-----
&P*Q
Addition
P
-----
PVQ
Leval 2:
DeMorgans theorms (DeM):
~(P*Q)+(~Pv~Q)
~(PvQ)+(~P*~Q)
Commutation (com.):
(PvQ)+(QvP)
(P*Q)+(Q*P)
Association (assoc):
[Pv(QvR)]+[(PvQ)vR]
[P*(RvR)]+[(P*Q)*R]
Distribution (dist.):
[P*(QvR)]+[(P*Q)v(P*R)]
[Pv(Q*R)]+[(PvQ)*(PvR)]
Double Negation (DN):
P+~~P
Transposition (trans):
(P>Q)+(~Q>~P)
Material Implication (Impl):
(P>Q)+(~PvQ)
Material Equivilance (equiv):
(P=Q)+[(P>Q)*(Q>P)]
(P=Q)+[(P*Q)v(~P*~Q)]
Exportation (exp):
[(P*Q)>R]+[P>(Q>R)]
Tautology (taut):
P+(PvP)
P+(P*P)
When leaving a problem please state weather its a leval one (using only he codes in leval one) or leval two, using codes from both potentially.
Jez, nothing from the hw please unless we've already done it in class, this is just for fun.
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Posted: Mon Oct 17, 2005 10:47 am
An example:
Problem -
P>Q
Q>R
P
Prove R
Awnser
P>Q Given
Q>R Given
P>R H.S.
P Given
--------------
& R Modus Ponens
Got it? Good heres the first example....
P*Q
P>Q
Q>R
R>S
Prove S
heart
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Posted: Sun Dec 11, 2005 12:42 am
crying You didn't say there was gonna be maaaath. xp
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Posted: Fri Dec 16, 2005 12:28 am
According to my schedual this is philosphy not math, now play! heart
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