Lewis Carroll Logic Problems

The original problem has 25 premisses and 28 attributes

Number	Premiss
1	Tall men, who drive about in carriages, are cheered by the little boys;
2	Men with blue eyes, who like running across a ploughed field, are worth looking at;
3	All the grocers in the street have grey hair;
4	A man, who is listened to with respect, can influence others;
5	Men with long beards, who look like patriarchs, are all Jews;
6	A tall man, who has sprained his ankle, walks lame;
7	Rbeumatic men, who are fond of arm-chairs, are fretful;
8	All men, who are over ninety years old, are wrinkled;
9	No influential man, who is cheered by little boys, is an object of scorn;
10	Men, who hold up their heads, are fascinating, provided that they have blue eyes;
11	All the men in this street, who have long beards, look like goats;
12	All short wise-looking men are grocers;
13	A wrinkled grey-haired man is always fond of an arm-chair;
14	A man, who is fit to be a judge and is cheered by the little boys, is always conceited;
15	All grocers have blue eyes and long beards;
16	Wise-Iooking men are always listened to with respect;
17	All men, who are Jews, and who look like goats, suffer from rheumatism;
18	All the tall men in this street are fit to be judges;
19	No grey-haired man is fascinating if he is fretful;
20	Conceited men, who drive in carriages, are objects of scorn;
21	No man in this street is worth looking at unless he holds up his head;
22	All wrinkled men look wise;
23	A man, who looks like a goat, is not listened to with respect, unless he also looks like a patriarch;
24	A man, who is fit to be a judge and who can influence others, drives about in a carriage if he happens to walk lame.

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

Attribute symbol	Attribute
A	liking to run across a ploughed field
B	listened to with respect
C	looking like a goat
D	looking like a patriarch
E	looking wise
F	objects of scorn
G	over ninety
H	rheumatic
L	tall
M	walking lame
N	worth looking at
P	wrinkled
a	blue-eyed
b	cheered by the little boys
c	conceited
d	driving about in a carriage
e	fascinating
h	fit to be a judge
k	fond of arm-chairs
l	fretful
m	grey-haired
n	grocers
r	having a long beard
s	having sprained his ankle
t	holding up his head
v	influential
w	in this street
z	Jews

So the symbolic form of the premisses is as follows:

Premiss. There are no men that are	Symbolic form of premiss
1. tall, driving about in a carriage, not cheered by the little boys,	Ldb'
2. blue-eyed, liking to run across a ploughed field, not worth looking at,	aAN'
3. grocers, in this street, not grey-haired,	nwm'
4. listened to with respect, not influential,	Bv'
5. having a long beard, looking like a patriarch, not Jews,	rDz'
6. tall, having sprained his ankle, not walking lame,	LsM'
7. rheumatic, fond of arm-chairs, not fretful,	Hkl'
8. over ninety, not wrinkled,	GP'
9. cheered by the little boys, influential, objects of scorn,	vbF
10. blue-eyed, holding up his head, not fascinating,	tae'
11. in this street, having a long beard, not looking like a goat,	wrC'
12. not tall, not grocers, looking wise,	L'En'
13. grey-haired, not fond of arm-chairs, wrinkled,	Pmk'
14. cheered by the little boys, fit to be a judge, not conceited,	hbc'
15. not blue-eyed, grocers,	na'
16. grocers, not having a long beard,	nr'
17. not listened to with respect, looking wise,	EB'
18. Jews, not rheumatic, looking like a goat,	zCH'
19. tall, not fit to be a judge,	Lh'
20. grey-haired, fretful, fascinating,	mle
21. driving about in a carriage, not objects of scorn, conceited,	cdF'
22. worth looking at, in this street, not holding up his head,	wt'N
23. wrinkled, not looking wise,	PE'
24. listened to with respect, not looking like a patriarch, looking like a goat,	CD'B
25. not driving about in a carriage, influential, walking lame, fit to be a judge,	hvMd'

The registry is:

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

and the barred premises are as follows:

1	barred by	9 14
3	barred by	13 20
4	barred by	9 25
8	barred by	13 23
11	barred by	18 24
12	barred by	1 6 19
15	barred by	2 10
16	barred by	5 11
17	barred by	4 24
19	barred by	14 25
23	barred by	12 17
25	barred by	1 21

Solution to be tested is AwsG

This document was last updated 7 September 2020

Index of Logic Problems