For those who commented on my previous questions, sorry for the lack of information and explanation. Clearly I did not do a good job of explaining myself so I deleted the question and hope this one goes better.
EDIT: here is what I have so far, can anyone tell me if it is right/wrong? http://www.box.net/shared/static/hrv9rh7ukt.jpg
I know how to perform standard tree method satisfiable tests but this question I am having trouble with because it has to do with elections.
Question:
Use the tree method to determine whether or not the following set of sentences is statisfialbe. If so, specify a satisfying case for its atomic sentences (ie aRjb, dRic, bRja, and cPid).
{bRja $\rightarrow$ dRic, dRic $\rightarrow$ $\neg$cPid, dRic $\rightarrow$ aRjb, $\neg$dRic $\rightarrow$ cPid, cPid $\rightarrow$ bRja, aRjb $\rightarrow$ cPid}
I think the format of the sentences is standard nomenclature but if it is not, ill will do my best to explain it. P refers to Social Preternce while R refers to Rule.
UPDATE:
I set the following
A = aRjb
B = bRja
C = cPid
D = dRic
So then the tree looks like:
- $B \lor D$
- $D \lor \neg C$
- $D \lor A$
- $D \lor C$
- $C \lor B$
- $A \lor C$
Maybe its because I haven't done even standard tree methods in a while but can anyone help me on how to check if it is satisfiable?
EDIT UPDATE:
bPia $\rightarrow$ cPia
aPic $\rightarrow$ (aPib $\lor$ bPic)
Conc, ($\neg$aPib $\land$ $\neg$bPia) $\land$ ($\neg$aPic $\land$ $\neg$cPia) $\rightarrow$ ($\neg$aPic $\land$ $\neg$cPia)
Can I solve it like the rest by substituting each "clause" with a letter?
So I would set bPia to B1, bPic to B2, cPia to B1, aPib to A1, aPic to A2, and solve like a normal tree?