Lewis Carroll Logic Problems

The original problem has 25 premisses and 27 attributes

Number	Premiss
1	A quarrelsome man does not deserve blame if he is not in his right mind;
2	Men, who are objects of terror, are always avoided;
3	The popular candidates in this election are Liberals;
4	Captains always tell long yarns;
5	A man of slim figure, who is constantly quoted as a model-citizen, is always conceited;
6	Any man of genial manners may safely go through the town today except Mr. Brown;
7	No good man of business, who is cautious as to what he states, ever says he has seen the sea-serpent;
8	A thoughtless man is a constant cause of mischief;
9	A popular man, who is fat, is always out of breath;
10	A man, who tells long yarns and has no geniality of manner, is an object of terror;
11	Mr. Brown is a candidate in this election;
12	A man, who is ready to make amends for any harm he has done, is always a humble man;
13	No man, who tells long yarns without giving names or dates, is readiIy believed;
14	No quarrelsome man would be safe in the streets today, unless he were a candidate in this election;
15	A good business-man, who is not quarrelsome, is cautious as to everything he states;
16	No man ever tells long yarns, when running to catch a train and out of breath;
17	A man, who is a constant cause of mischief and is not ready to make amends for the harm he has done, cannot be in his right mind;
18	No man, who gives names and dates, is avoided, unless he is in his second childhood;
19	The Liberal candidates in this election are all running to catch the train;
20	Any man, who gives names and dates, is a good man of business;
21	No quarrelsome man is an object of terror if he is in his second childhood;
22	A man deserves blame if he is not ready to make amends for any harm he has done;
23	A man who tells long yarns is always popular;
24	A man of genial manners, who is ready to make amends for any harm he has done, is constantly quoted as a model-citizen.

The universe of discourse is men . We will use the following dictionary:

Attribute symbol	Attribute
A	out of breath
B	popular
C	quarrelsome
D	readily believed
E	ready to make amends for any harm he has done
F	running to catch a train
G	safe in the streets to-day
H	sane
J	saying that he has seen the sea-serpent
L	telling long yarns
M	thoughtful
a	avoided
b	Brown
c	candidates in this election
d	captains
e	cautious in making statements
h	conceited
k	constantly causing mischief
l	constantly quoted as a model-citizen
m	deserving blame
n	fat
r	genial
s	giving narnes and dates
t	good men of business
v	in his second childhood
w	Líberals
z	objects of terror

So the symbolic form of the premisses is as follows:

Premiss. There are no men that are	Symbolic form of premiss
1. quarrelsome, not sane, deserving blame,	CH'm
2. objects of terror, not avoided,	za'
3. popular, not Líberals,	Bw'
4. captains, not telling long yarns,	dL'
5. not fat, constantly quoted as a model-citizen, not conceited,	n'lh'
6. genial, safe in the streets to-day, Brown,	rGb
7. good men of business, cautious in making statements, saying that he has seen the sea-serpent,	teJ
8. not thoughtful, not constantly causing mischief,	M'k'
9. popular, fat, not out of breath,	BnA'
10. not objects of terror, telling long yarns, not genial,	Lr'z'
11. Brown, not candidates in this election,	bc'
12. conceited, ready to make amends for any harm he has done,	Eh
13. telling long yarns, not giving narnes and dates, readily believed,	Ls'D
14. quarrelsome, safe in the streets to-day, not candidates in this election,	CGc'
15. not quarrelsome, good men of business, not cautious in making statements,	tC'e'
16. telling long yarns, out of breath, running to catch a train,	LFA
17. sane, constantly causing mischief, not ready to make amends for any harm he has done,	kE'H
18. avoided, giving narnes and dates, not in his second childhood,	sav'
19. Líberals, candidates in this election, not running to catch a train,	cwF'
20. not good men of business, giving narnes and dates,	st'
21. quarrelsome, objects of terror, in his second childhood,	Czv
22. not deserving blame, not ready to make amends for any harm he has done,	E'm'
23. not popular, telling long yarns,	LB'
24. not constantly quoted as a model-citizen, genial, ready to make amends for any harm he has done,	rEl'
25. not genial, Brown,	br'

The registry is:

Entity	Appears in	Complement appears in
A	16	9
B	3 9	23
C	1 14 21	15
D	13
E	12 24	17 22
F	16	19
G	6 14
H	17	1
J	7
L	10 13 16 23	4
M		8
a	18	2
b	6 11 25
c	19	11 14
d	4
e	7	15
h	12	5
k	17	8
l	5	24
m	1	22
n	9	5
r	6 24	10 25
s	18 20	13
t	7 15	20
v	21	18
w	19	3
z	2 21	10

and the barred premises are as follows:

4	barred by	10 13 16 23
10	barred by	2 21
13	barred by	18 20
15	barred by	1 14 21
19	barred by	11 14
20	barred by	7 15
23	barred by	3 9

Solution to be tested is dGbJM'D

This document was last updated 7 September 2020

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