Someone living in a mansion has killed Aunt Anna.
- Anna, Cal, and the butler live in the mansion, and are the only people who live therein.
- A killer always hates his victim, and is never richer than his victim.
- Cal hates no one that Aunt Anna hates.
- Anna hates everyone except the butler.
- The butler hates everyone not richer than Aunt Anna.
- The butler hates everyone Anna hates.
- No one in the mansion hates everyone else..
Who killed Aunt Anna?
Only the 'else' in the expression 'everyone else' of premise 7 is wrong, that is: (7) 'No one in the mansion hates everyone' would be correct. Now, there is no contradiction left.
From (4) follows
(8) hates(anna,anna) & hates(anna,cal) & not hates(anna,butler)
From (3) follows
(9) not hates(cal,anna) & not hates(cal,cal)
From (2) and (9) follows
(10) not killed(cal,anna)
From (6) and (8) follows
(11) hates(butler,anna) & hates(butler,cal)
From (7) and (11) follows
(12) not hates(butler,butler)
From the Contraposition (Cp) of (5)
(5) not richer_than(X,anna) --> hates(butler,X)
(Cp) not hates(butler,X) --> richer_than(X,anna)
and (12) follows
From (2) and (13) follows
(14) not killed(butler,anna)
From (1), (2), (10), and (14) follows
Edited on November 27, 2016, 12:20 pm
Edited on December 2, 2016, 3:47 am
Edited on December 2, 2016, 4:06 am
Posted by ollie
on 2016-11-27 11:56:53