Lewis Carroll Logic Problems

The original problem has 39 premisses and 43 attributes

Number	Premiss
1	All Jews wear beards;
2	No learned traveler cares for pitch-and-toss ;
3	All Frenchmen walk fast;
4	A good-humoured cab-driver is always graceful;
5	The house is empty, unless Ebenezer is in it;
6	No discontented person is interesting, unless he has traveled a good deal;
7	Those who can see always avoid pigs;
8	People with heads on their shoulders are not irritating, so long as they do not talk too much;
9	A Gentile, who is easily taken in, ought not to buy a horse;
10	Any one, who is willing to be painted green, is a discontented idiot;
11	No one of learning, if very remarkable, travels much;
12	Any one, who has not been educated by a pig, will take to smoking, unless he is threatened with a blunderbuss ;
13	All, who are not in the house, have heads on their shoulders;
14	Nothing but a pig can be made into bacon;
15	The learned are always interesting;
16	No squinting Jew is fond of pigs;
17	Those, who wear beards and look shy, are in failing health ;
18	Any one, who looks anxious, is an irritating bore;
19	All idiots are fretful and troublesome;
20	When a cab-driver retires from business, he is always threatened with a blunderbuss;
21	None but Frenchmen are fat and yet graceful;
22	Those, who wear beards, always retire from business when their health fails;
23	Gentiles are easily taken in;
24	Any fretful creature, that grunts, can be made into bacon;
25	Those who are dull are not troublesome, so long as they have some sense in their heads;
26	Those, who are fat and wish to ride, are always good-hurnoured;
27	Those, who are unlearned, but still avoid pigs, have some sense in their heads;
28	Any one, who is willing to be painted green and does not care for pitch-and-toss, is very remarkable ;
29	A talkative cab-driver is never a bore;
30	All bearded Frenchmen, who squint, are fond of pigs;
31	A Jewish cab-driver always looks shy;
32	Ebenezer will never take to smoking, unless he is threatened with a blunderbuss;
33	No fat pigs walk fast;
34	The unlearned are always dull;
35	Creatures, that are not pigs, but have been educated by pigs, always grunt;
36	Those, who have heads on their shoulders, always look anxious;
37	Any one, who is blind and easily taken in, may buy a horse, provided he does not wish to ride;
38	All pigs are fat;
39
40	N.B. Two of these Premisses are superfluous. Which are they?]

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

Attribute symbol	Attribute
A	having a head on his shoulders
B	having some sense in his head
C	idiots
D	interesting
E	in the house
F	very remarkable
G	irritating
H	Jews
J	learned
K	walking fast
L	looking anxious
M	looking shy
N	pigs
P	retiring from business
Q	smokers
R	squinting
T	talkative
V	willing to be painted green
W	wishing to ride.
X	threatened with a blunderbuss
a	able to see
b	avoiding pigs
c	bearded
d	bores
e	cab-drivers
f	capable of being made into bacon
g	travellers
h	caring for pitch-and-toss
j	contented
k	creatures who may buy a horse
l	dull
m	easily taken
n	Ebenezer
p	educated by a pig
q	failing in health
r	fat
s	fond of pigs
t	Frenchmen
u	troublesome
v	fretful
w	good-humoured
y	graceful
z	grunting

So the symbolic form of the premisses is as follows:

Premiss. There are no creatures that are	Symbolic form of premiss
1. Jews, not bearded,	Hc'
2. learned, travellers, caring for pitch-and-toss,	Jgh
3. Frenchmen, not walking fast,	tK'
4. cab-drivers, good-humoured, not graceful,	ewy'
5. not Ebenezer, in the house,	n'E
6. not travellers, interesting, not contented,	Dj'g'
7. able to see, not avoiding pigs,	ab'
8. having a head on his shoulders, not talkative, irritating,	AT'G
9. not Jews, easily taken, creatures who may buy a horse,	H'mk
10. not contented, willing to be painted green, not idiots,	VC'j'
11. learned, travellers, very remarkable,	JFg
12. not educated by a pig, smokers, threatened with a blunderbuss,	p'QX
13. not in the house, not having a head on his shoulders,	E'A'
14. not pigs, capable of being made into bacon,	N'f
15. learned, not interesting,	JD'
16. Jews, squinting, fond of pigs,	RHs
17. bearded, looking shy, not failing in health,	Mcq'
18. not irritating, looking anxious, not bores,	LG'd'
19. idiots, not fretful,	Cv'
20. cab-drivers, not threatened with a blunderbuss, retiring from business,	ePX'
21. not Frenchmen, graceful, fat,	ryt'
22. bearded, failing in health, not retiring from business,	cqP'
23. not Jews, not easily taken,	H'm'
24. not capable of being made into bacon, fretful, grunting,	vzf'
25. dull, not troublesome, not having some sense in his head,	lu'B'
26. not good-humoured, fat, wishing to ride. ,	rWw'
27. not learned, avoiding pigs, not having some sense in his head,	J'bB'
28. not caring for pitch-and-toss, willing to be painted green, not very remarkable,	Vh'F'
29. cab-drivers, talkative, bores,	eTd
30. Frenchmen, squinting, not fond of pigs,	tRs'
31. Jews, cab-drivers, not looking shy,	HeM'
32. Ebenezer, smokers, not threatened with a blunderbuss,	nX'Q
33. not walking fast, pigs, fat,	rNK'
34. not learned, not dull,	J'l'
35. educated by a pig, not pigs, not grunting,	N'pz'
36. having a head on his shoulders, not looking anxious,	AL'
37. not able to see, easily taken, creatures who may buy a horse, wishing to ride. ,	a'mWk
38. pigs, not fat,	Nr'
39. idiots, not troublesome,	Cu'

The registry is:

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

and the barred premises are as follows:

1	barred by	17 22
6	barred by	2 11
10	barred by	19 39
12	barred by	20 32
13	barred by	8 36
21	barred by	3 30
23	barred by	9 37
38	barred by	21 26 33

Solution to be tested is K'ej'kVQRu'B'W

This document was last updated 7 September 2020

Index of Logic Problems