# Caesar murder logic problem

it is a problem of logic concerning who killed Julius Caesar.
I have written the logical sentences and build the truth table, but I cannot find a way to combine all these...

p: Marcus Antonius(says): Cassius or Brutus or both
q: Cassius(says): not me. Marcus Antonius is lying
r: Brutus(says): if I did it, then the other two are guilty also.

m: Marcus Antonius is guilty
c: Cassius is guilty
b: Brutus is guilty

A guilty person always lies.
A non-guilty person always tells the truth

p: c OR b OR (c AND b)
q: c’ AND m (because a guilty always lies)
r: b => (c AND m)

###### Who is Participating?

Commented:
So here's the main truth table. For the left three T means guilty. For the right three T means told the truth.
``````M	C	B	C v B	C' ^ p'	B' v (C ^ M)
T	T	T	T	F	T
T	T	F	T	F	T
T	F	T	T	F	F
T	F	F	F	T	T
F	T	T	T	F	F
F	T	F	T	F	T
F	F	T	T	F	F
F	F	F	F	T	T
``````
But if anyone is guilty, then they must be lying and the innocent are truthful so we can blank out all the rows where there are two Ts or two Fs in someone's columns.
``````
M	C	B	C v B	C' ^ p'	B' v (C ^ M)
T	T	T		F
T	T	F		F	T
T	F	T			F
T	F	F	F	T	T
F	T	T	T	F	F
F	T	F	T	F	T
F	F	T	T		F
F	F	F		T	T
``````
This leaves three valid possible scenarios
M did it
C and B did it
C did it
All three (and only these three) satisfy all the given conditions.
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Commented:
not sure about the truth table, but... if marcus antonious did it, his statement being a lie and the other two being true is consistant.
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Commented:
Cassius being guilty is also consistent.
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Author Commented:
I understand the hole concept, but what is the answer?
We have only 1 answer, or not?
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Commented:
The way you have defined the problem yields three possible answers. If the question implies there is one answer, then please check to make sure you haven't missed anything. If you look at the three scenarios I listed, all of them work given the criteria in your original post.
So there are three possible answers.
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Author Commented:
There is one more sentence: only one of the persons is telling the truth, so, at line 5, Brutus is guilty, and what he says is false, so this is the solution...
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Commented:
I see. If only one is telling the truth, then there must be two guilty ones. So it's C and B (which is line 7 in the second table).
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Author Commented:
yes, at line 7...thank you...
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