Lewis Carroll Logic Problems

The original problem has 50 premisses and 52 attributes

Number	Premiss
1	I don't like walking with any London-friend of mine, unless he wears a tall hat;
2	The Colonel is ready to play billiards with any man who is not the subject of general conversation, unless he happens to be fat;
3	A man, who knows what o'clock it is and who never yields to me in argument, is unattractive;
4	No old tight-rope-dancer ever rouses me to enthusiasm;
5	Any novelist, whom I take pleasure in cutting, always cuts me dead;
6	A man, who goes about in kid-gloves, but without his coat, is a humbug;
7	All my intimate friends in London are young men;
8	No man, who is the subject of general conversation, ever rouses me to enthusiasm, unless he is a horsey man;
9	A man, who has his wits about him and does not choose his own wines, is always "at home" when I call;
10	A man, who is a good shot and never tells pointless anecdotes, is sure to have a good temper;
11	All humbugs, who write novels, are intimate friends of mine;
12	I like to walk with a good-tempered man, unless he goes about in his shirt-sleeves;
13	A man, who never loses his umbrella, and is not easily taken in, is sure to be an early riser;
14	Fat men, who do not dance on the tight-rope, are universally respected;
15	I regard with contemptuous pity a man who fails in life, and who runs across the street;
16	A man, who does not stick to business, is not likely to be elected Mayor, unless he has bushy whiskers;
17	An elephant hunter always rouses me to enthusiasm, unless he happens to be a farmer;
18	Any London friend of mine, who tells pointless anecdotes, is a humbug;
19	I never invite an old man to dinner, unless he has lent me money;
20	A man, who does not stick to business, does not run across the street, and has bushy hair, is in no danger of getting a bad fall;
21	A man, who gets up late and sometimes loses his umbrella, has little chance of marrying an heiress;
22	An old man, who cares for appearances, always wears kid-gloves;
23	A good-tempered man never cuts me dead, unless he is a humbug;
24	A man, who never tells pointless anecdotes and has never lent me money, has his wits about him;
25	A man, who chooses his own wines and always yields to me in argument, is the sort that I invite to dine with me;
26	I always try to be civil to a man who fails in life, unless he has bushy whiskers;
27	All farmers are horsey men;
28	A novelist is a dull companion, unless he rouses me to enthusiasm;
29	All men, who get up early, and stick to business and win universal respect, are rich;
30	Any London friend of mine, to whom I try to be civil, will probably be elected Mayor;
31	Any good-tempered man, who has lent me money and does not care for appearances, is willing to shake hands with me when I am in rags;
32	The only men, with whom the Colonel will play billiards, are either horsey men or farmers ;
33	I always invite an attractive man to dine with me, provided he is rich;
34	A man, who is apt to walk on tip-toe and whom I regard with contemptuous pity, is sure to be one who sticks to business;
35	The only men, who are always "at home" to me, but whom I never invite to dinner, are magistrates;
36	I always make an intimate friend of a man who will shake hands with me when I am in rags and will give up his umbrella to me when it is raining;
37	Any London friend of mine, who understands horses, is universally respected;
38	An unattractive man, who chooses his own wines, is easily taken in;
39	I have sufficient courage to insult any novelist, unless he happens to be a good shot;
40	An old man, who is apt to walk on tip-toe, will probably get a bad fall;
41	A man, who never knows what o'clock it is, and who has never lent me money, will probably marry an heiress;
42	No London-friend of mine, who has his wits about him, is easily taken in;
43	I never forget any old man who is willing to shake hands with me when I am in rags;
44	A novelist, who does not stick to business, is sure to fail in life;
45	I do not dare to insult an ill-tempered man, unless he happens to be an intimate friend of mine;
46	Those magistrates, who will not shake hands with me when I am in rags, always choose their own wine;
47	All dull companions are either horsey men or elephant-hunters;
48	Men, who wear tall hats and kid gloves, always cut me dead;
49	A man, who has bushy whiskers and is universally respected, is apt to walk on tip-toe;
50	I delight in cutting a man, whom I perfectly remember, but who will not give up his umbrella to me when it is raining.

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

Attribute symbol	Attribute
A	London-friends of mine
B	magistrates
C	men to whom I try to be civil
D	men who cut me
E	men who have lent me money
F	men whom I dare insult
G	men whom I delight to cut
H	men with whom I like to walk
I	willing to shake hands with me when I am in rags
J	men with whom the Colonel is willing to play billiards
K	novelists
L	old
M	regarded by me with contemptuous pity
N	remembered by me
O	yielding to me in argument
P	rich
Q	rousing me to enthusiasm
R	running across a street
S	sometimes losing his umbrella
T	sticking to business
U	subjects of general conversation
V	successful in life
W	tight-rope dancers
X	universally respected
Y	wearing a coat
Z	wearing a tall hat
a	apt to tell pointless anecdotes
b	apt to walk on tip-toe
c	"at home " to me
d	attractive
e	caring for appearances
f	choosing his own wines
g	dull companions
h	early risers
i	wearing kid gloves
j	easily taken in
k	elephant-hunters
l	farmers
m	fat
n	good shots
o	willing to give up umbrella to me when it is raining
p	good-tempered
q	having bushy whiskers
r	having his wits about him
s	horsey
t	humbugs
u	intimate friends of mine
v	invited to dine with me
w	knowing what o'clock it is
x	likely to be elected Mayor
y	likely to get a bad fall
z	likely to marry an heiress

So the symbolic form of the premisses is as follows:

Premiss. There are no men that are	Symbolic form of premiss
1. men with whom I like to walk , London-friends of mine, not wearing a tall hat,	HAZ'
2. not men with whom the Colonel is willing to play billiards, not subjects of general conversation, not fat,	J'U'm'
3. knowing what o'clock it is, not yielding to me in argument, attractive,	wO'd
4. tight-rope dancers, old, rousing me to enthusiasm,	WLQ
5. novelists, men whom I delight to cut, not men who cut me,	KGD'
6. wearing kid gloves, not wearing a coat, not humbugs,	iY't'
7. London-friends of mine, old, intimate friends of mine,	uAL
8. subjects of general conversation, rousing me to enthusiasm, not horsey,	UQs'
9. having his wits about him, not choosing his own wines , not "at home " to me,	rf'c'
10. good shots, not apt to tell pointless anecdotes, not good-tempered,	na'p'
11. novelists, humbugs, not intimate friends of mine,	tKu'
12. men with whom I like to walk , not wearing a coat, good-tempered,	HpY'
13. not sometimes losing his umbrella, not easily taken in, not early risers,	S'j'h'
14. fat, not tight-rope dancers, not universally respected,	mW'X'
15. not regarded by me with contemptuous pity, not successful in life, running across a street,	M'V'R
16. not sticking to business, not having bushy whiskers, likely to be elected Mayor,	T'q'x
17. not rousing me to enthusiasm, elephant-hunters, not farmers,	kQ'l'
18. London-friends of mine, not humbugs, apt to tell pointless anecdotes,	Aat'
19. old, invited to dine with me, not men who have lent me money,	LvE'
20. not running across a street, not sticking to business, having bushy whiskers, likely to get a bad fall,	T'R'qy
21. sometimes losing his umbrella, not early risers, likely to marry an heiress,	h'Sz
22. old, not wearing kid gloves, caring for appearances,	Lei'
23. men who cut me, not humbugs, good-tempered,	pt'D
24. not having his wits about him, not apt to tell pointless anecdotes, not men who have lent me money,	a'E'r'
25. yielding to me in argument, choosing his own wines , not invited to dine with me,	fOv'
26. not successful in life, not having bushy whiskers, not men to whom I try to be civil,	C'V'q'
27. not horsey, farmers,	ls'
28. not rousing me to enthusiasm, novelists, not dull companions,	Kg'Q'
29. early risers, universally respected, sticking to business, not rich,	hTXP'
30. London-friends of mine, not likely to be elected Mayor, men to whom I try to be civil,	ACx'
31. good-tempered, men who have lent me money, not caring for appearances, not willing to shake hands with me when I am in rags,	pEe'I'
32. men with whom the Colonel is willing to play billiards, not horsey, not farmers,	Js'l'
33. attractive, not invited to dine with me, rich,	dPv'
34. regarded by me with contemptuous pity, not sticking to business, apt to walk on tip-toe,	bMT'
35. "at home " to me, not invited to dine with me, not magistrates,	cv'B'
36. not intimate friends of mine, willing to shake hands with me when I am in rags, willing to give up umbrella to me when it is raining,	u'Io
37. London-friends of mine, horsey, not universally respected,	AsX'
38. not attractive, choosing his own wines , not easily taken in,	d'fj'
39. novelists, not good shots, not men whom I dare insult,	KF'n'
40. old, not likely to get a bad fall, apt to walk on tip-toe,	Lby'
41. not knowing what o'clock it is, not men who have lent me money, not likely to marry an heiress,	w'E'z'
42. London-friends of mine, having his wits about him, easily taken in,	Arj
43. old, willing to shake hands with me when I am in rags, not remembered by me,	LN'I
44. novelists, successful in life, not sticking to business,	KT'V
45. not intimate friends of mine, not good-tempered, men whom I dare insult,	p'Fu'
46. not choosing his own wines , not willing to shake hands with me when I am in rags, magistrates,	BI'f'
47. not horsey, not elephant-hunters, dull companions,	gs'k'
48. wearing a tall hat, not men who cut me, wearing kid gloves,	ZiD'
49. universally respected, having bushy whiskers, not apt to walk on tip-toe,	qXb'
50. not men whom I delight to cut, not willing to give up umbrella to me when it is raining, remembered by me,	G'No'

The registry is:

Entity	Appears in	Complement appears in
A	1 7 18 30 37 42
B	46	35
C	30	26
D	23	5 48
E	31	19 24 41
F	45	39
G	5	50
H	1 12
I	36 43	31 46
J	32	2
K	5 11 28 39 44
L	4 7 19 22 40 43
M	34	15
N	50	43
O	25	3
P	33	29
Q	4 8	17 28
R	15	20
S	21	13
T	29	16 20 34 44
U	8	2
V	44	15 26
W	4	14
X	29 49	14 37
Y		6 12
Z	48	1
a	18	10 24
b	34 40	49
c	35	9
d	3 33	38
e	22	31
f	25 38	9 46
g	47	28
h	29	13 21
i	6 48	22
j	42	13 38
k	17	47
l	27	17 32
m	14	2
n	10	39
o	36	50
p	12 23 31	10 45
q	20 49	16 26
r	9 42	24
s	37	8 27 32 47
t	11	6 18 23
u	7	11 36 45
v	19	25 33 35
w	3	41
x	16	30
y	20	40
z	21	41

and the barred premises are as follows:

7	barred by	11 36 45
11	barred by	6 18 23
18	barred by	10 24
19	barred by	25 33 35
22	barred by	6 48
23	barred by	5 48
24	barred by	9 42
27	barred by	17 32
29	barred by	16 20 34 44
31	barred by	19 24 41
37	barred by	8 27 32 47
38	barred by	3 33
42	barred by	13 38
44	barred by	15 26
49	barred by	34 40

Solution to be tested is HALKY'

This document was last updated 7 September 2020

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