Lewis Carroll Logic Problems

The original problem has 36 premisses and 38 attributes

Number	Premiss
1	All whom I have taught, except my own sons, know something;
2	A contented barber is a welcome visitor;
3	All, except those who are in this house, are good scholars;
4	All the dandies, who have been plucked, are grinning;
5	Any one, who admires a bald head, is either a brother of mine or is in good spirits;
6	Those, who do not think intensely, know nothing;
7	Nobody with a headache likes beating a gong;
8	Any one in this house, who makes foolish remarks, is a son of mine;
9	None who value health like toffy;
10	All barbers wear white aprons;
11	A fanciful man, who does not read hard, is always complaining;
12	Peter is a candidate for Matriculation;
13	All, who do little, except my sons, are contented;
14	The candidates for Responsions, who have not been plucked, are all in good spirits;
15	No son of' mine, who is in good health, is a dandy;
16	Good scholars, who think intensely but have no self-respect, are boastful;
17	My brothers are al! barbers;
18	Any one, who wears a white apron and can endure a hurdy-gurdy, is worthy of honour;
19	Nobody, who respects himself, dances jigs while at lessons;
20	Those of my sons, who are always complaining, are ambitious men;
21	All the hard-reading men, who have been plucked, are dandies;
22	All barbers, who are worthy of honour, dance jigs;
23	Any one, who has a headache, either thinks intensely or is one of my old pupils;
24	Boasters do little;
25	Those, who do not value their health, like beating a gong when they are not at lessons;
26	All, except good scholars, make foolish remarks;
27	Those, who respect themselves, are mild in manner;
28	All my sons, except Peter, are candidates for Responsions;
29	Barbers, who grin, are in good health;
30	Any one in good spirits, who does not like beating a gong, cannot endure a hurdy-gurdy;
31	All ambitious men read hard ;
32	All candidates for Matriculation have been plucked;
33	No boaster is a welcome visitor;
34	All persons, who are mild in manner, except my sons, like toffy;
35	Any one, who does not admire a bald head, is a barber;
36	All, who indulge in reverie, are fanciful men

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

Attribute symbol	Attribute
A	healthy
B	indulging in reverie
C	in good spirits
D	in this house
E	knowing something
F	liking to beat a gong
G	liking toffy
H	making foolish remarks
J	mild in manner
L	my brothers
M	my sons
N	Peter
P	plucked
Q	self-respecting
R	taught by me
T	thinking intensely
V	valuing health
W	wearing a white apron
X	welcome visitors
Y	worthy of honour.
a	able to endure a hurdy-gurdy
b	admiring a bald head
c	ambitious men
d	at lessons
e	barbers
h	boasters
k	candidates for Matriculation
l	candidates for Responsions
m	complaining
n	contented
r	dancing jigs
s	dandies
t	doing little
u	fanciful men
v	good scholars
w	grinning
x	hard-reading men
z	having a headache

So the symbolic form of the premisses is as follows:

Premiss. There are no persons that are	Symbolic form of premiss
1. taught by me, not my sons, not knowing something,	RM'E'
2. contented, barbers, not welcome visitors,	neX'
3. not in this house, not good scholars,	D'v'
4. dandies, plucked, not grinning,	sPw'
5. not barbers, admiring a bald head, not my brothers,	bL'e'
6. knowing something, not thinking intensely,	T'E
7. having a headache, liking to beat a gong,	zF
8. not my sons, in this house, making foolish remarks,	DHM'
9. valuing health, liking toffy,	VG
10. barbers, not wearing a white apron,	eW'
11. fanciful men, not hard-reading men, not complaining,	ux'm'
12. Peter, not candidates for Matriculation,	Nk'
13. not my sons, not contented, doing little,	tM'n'
14. not barbers, not plucked, candidates for Responsions,	lP'e'
15. my sons, dandies, healthy,	MAs
16. good scholars, thinking intensely, not self-respecting, not boasters,	vTQ'h'
17. not barbers, my brothers,	Le'
18. wearing a white apron, able to endure a hurdy-gurdy, not worthy of honour. ,	WaY'
19. self-respecting, dancing jigs, at lessons,	Qrd
20. my sons, complaining, not ambitious men ,	Mmc'
21. not dandies, plucked, hard-reading men,	xPs'
22. barbers, worthy of honour. , not dancing jigs,	eYr'
23. not taught by me, not thinking intensely, having a headache,	zT'R'
24. not doing little, boasters,	ht'
25. not liking to beat a gong, not valuing health, not at lessons,	V'd'F'
26. not good scholars, not making foolish remarks,	v'H'
27. self-respecting, not mild in manner,	QJ'
28. my sons, not Peter, not candidates for Responsions,	MN'l'
29. barbers, grinning, not healthy,	ewA'
30. not liking to beat a gong, able to endure a hurdy-gurdy, in good spirits,	CF'a
31. not hard-reading men, ambitious men ,	cx'
32. not plucked, candidates for Matriculation,	kP'
33. welcome visitors, boasters,	hX
34. not my sons, not liking toffy, mild in manner,	JM'G'
35. not barbers, not admiring a bald head,	b'e'
36. not fanciful men, indulging in reverie,	Bu'

The registry is:

Entity	Appears in	Complement appears in
A	15	29
B	36
C	30
D	8	3
E	6	1
F	7	25 30
G	9	34
H	8	26
J	34	27
L	17	5
M	15 20 28	1 8 13 34
N	12	28
P	4 21	14 32
Q	19 27	16
R	1	23
T	16	6 23
V	9	25
W	18	10
X	33	2
Y	22	18
a	18 30
b	5	35
c	31	20
d	19	25
e	2 10 22 29	5 14 17 35
h	24 33	16
k	32	12
l	14	28
m	20	11
n	2	13
r	19	22
s	4 15	21
t	13	24
u	11	36
v	16	3 26
w	29	4
x	21	11 31
z	7 23

and the barred premises are as follows:

7	barred by	25 30
16	barred by	19 27 6 23
21	barred by	4 15 11 31

Solution to be tested is zaCB

This document was last updated 7 September 2020

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