## Thursday, November 20, 2008

### Logic lesson

about conclusions of two hypothetical premisses including same two elemenatary hypothetic clauses:

((P>Q)&(P>-Q)) > -P
((P>Q)&(-P>Q)) > Q
((P>Q)&(-P>-Q)) > (P<>Q)
((P>Q)&(Q>P)) > (P<>Q)
((P>Q)&(Q>-P)) > -P
((P>Q)&(-Q>P)) > Q

((P>-Q)&(P>Q)) > -P
((P>-Q)&(-P>Q)) > (PAQ)
((P>-Q)&(-P>-Q)) > -Q
((P>-Q)&(Q>P)) > -Q
((P>-Q)&(-Q>P)) > (PAQ)
((P>-Q)&(-Q>-P)) > -P

((-P>Q)&(P>Q)) > Q
((-P>Q)&(P>-Q)) > (PAQ)
((-P>Q)&(-P>-Q)) > P
((-P>Q)&(Q>P)) > P
((-P>Q)&(Q>-P)) > (PAQ)
((-P>Q)&(-Q>-P)) > Q

((-P>-Q)&(P>Q)) > (P<>Q)
((-P>-Q)&(P>-Q)) > -Q
((-P>-Q)&(-P>Q)) > P
((-P>-Q)&(Q>-P)) > -Q
((-P>-Q)&(-Q>P)) > P
((-P>-Q)&(-Q>-P)) > (P<>Q)

P is an elementary hypothetical clause, if it stands in an hypothetical premiss like P>Q. So is Q.

-P is its contradictory opposite (add or take away a not inside the clause). As -Q is of Q.

(P>Q) means "P implies Q".
(Q>P) means "Q implies P".
(P<>Q) means "P and Q imply each other".
(PAQ) means "either P or Q but not both".

& means "and".

Note that 16 conclusions are categorical [like]:

"P is true."
"Q is true."
"P is not true."
"Q is not true."