Solved

Caesar murder logic problem

Posted on 2011-03-17
8
661 Views
Last Modified: 2012-05-11
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)

 
0
Comment
Question by:dimi67
8 Comments
 
LVL 4

Expert Comment

by:sgvill
Comment Utility
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.
0
 
LVL 84

Expert Comment

by:ozo
Comment Utility
Cassius being guilty is also consistent.
0
 
LVL 37

Accepted Solution

by:
TommySzalapski earned 500 total points
Comment Utility
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

Open in new window

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

Open in new window

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.
0
 

Author Comment

by:dimi67
Comment Utility
I understand the hole concept, but what is the answer?
We have only 1 answer, or not?
0
How your wiki can always stay up-to-date

Quip doubles as a “living” wiki and a project management tool that evolves with your organization. As you finish projects in Quip, the work remains, easily accessible to all team members, new and old.
- Increase transparency
- Onboard new hires faster
- Access from mobile/offline

 
LVL 37

Expert Comment

by:TommySzalapski
Comment Utility
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.
0
 

Author Comment

by:dimi67
Comment Utility
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...
0
 
LVL 37

Expert Comment

by:TommySzalapski
Comment Utility
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).
0
 

Author Comment

by:dimi67
Comment Utility
yes, at line 7...thank you...
0

Featured Post

Free Trending Threat Insights Every Day

Enhance your security with threat intelligence from the web. Get trending threat insights on hackers, exploits, and suspicious IP addresses delivered to your inbox with our free Cyber Daily.

Join & Write a Comment

Suggested Solutions

Introduction On a scale of 1 to 10, how would you rate our Product? Many of us have answered that question time and time again. But only a few of us have had the pleasure of receiving a stack of the filled out surveys and being asked to do somethi…
Foreword (May 2015) This web page has appeared at Google.  It's definitely worth considering! https://www.google.com/about/careers/students/guide-to-technical-development.html How to Know You are Making a Difference at EE In August, 2013, one …
Access reports are powerful and flexible. Learn how to create a query and then a grouped report using the wizard. Modify the report design after the wizard is done to make it look better. There will be another video to explain how to put the final p…
This video gives you a great overview about bandwidth monitoring with SNMP and WMI with our network monitoring solution PRTG Network Monitor (https://www.paessler.com/prtg). If you're looking for how to monitor bandwidth using netflow or packet s…

772 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question

Need Help in Real-Time?

Connect with top rated Experts

13 Experts available now in Live!

Get 1:1 Help Now