Lewis Carroll Logic Problems

The original problem has 22 premisses and 23 attributes

Number	Premiss
1	A grown-up man, who doubts that we are a free nation, is a simpleton
2	Any student of Modern History has heard of Magna Charta
3	Wilson is a thoughtful man;
4	A student of Ancient History, who does not know many attornies will have to push his own way in life
5	All rich men are worth knowing;
6	A simpleton who, not understanding Politics, talks about himself, is not a remarkable man;
7	Wilson doubts whether we are a free nation;
8	A student of Law is remarkable, if he never heard of Magna Charta;
9	A grown-up man, who does not study Modern History, cannot understand Politics;
10	A simpleton is likely to succeed at the Bar, if he knows many attornies;
11	Wilson is not a cricketer;
12	A minor, who doubts if we are a free nation, is not worth knowing;
13	All, who are likely to succeed at the Bar, study Law or Modern History;
14	A thoughtful man, who doubts if we are a free nation, is a dreamer who never reads the papers;
15	No clever man, who is grown up, talks about himself;
16	Dreamers, who are not cricketers, believe that cricket is extinct;
17	A simpleton, who is worth knowing, need not push his own way in life;
18	No one, who has heard of Magna Charta doubts that we are a free nation;
19	A man, who walks rather than take a cab, who believes that cricket is extinct, and who never reads the paper, is worth knowing.
20	Wilson is studying History;
21	A poor man will walk rather than take a cab.

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

Attribute symbol	Attribute
A	studying Law
B	talking about himself
C	thoughtful
D	understanding Politics
E	willing to walk rather than take a cab
F	Wilson
G	worth knowing.
a	believing that cricket is extinct
b	clever
c	cricketers
d	doubting whether we are a free nation
e	dreamers
h	grown-up
k	having heard of Magna Charta
l	knowing many attornies
m	likely to succeed at the Bar
n	needing to push his own way in life
r	reading the papers
s	remarkable
t	rich
v	simpletons
w	studying Ancient History
z	studying Modern History

So the symbolic form of the premisses is as follows:

Premiss. There are no men that are	Symbolic form of premiss
1. grown-up , doubting whether we are a free nation, not simpletons,	hdv'
2. studying Modern History , not having heard of Magna Charta ,	zk'
3. Wilson, not thoughtful,	FC'
4. studying Ancient History, not knowing many attornies , not needing to push his own way in life,	wl'n'
5. rich, not worth knowing.,	tG'
6. simpletons, not understanding Politics , talking about himself, remarkable,	vD'Bs
7. not doubting whether we are a free nation, Wilson,	Fd'
8. not having heard of Magna Charta , not remarkable, studying Law ,	Ak's'
9. grown-up , not studying Modern History , understanding Politics ,	hz'D
10. simpletons, knowing many attornies , not likely to succeed at the Bar ,	vlm'
11. Wilson, cricketers,	Fc
12. not grown-up , doubting whether we are a free nation, worth knowing.,	h'dG
13. not studying Modern History , not studying Law , likely to succeed at the Bar ,	A'z'm
14. doubting whether we are a free nation, thoughtful, not dreamers,	Cde'
15. grown-up , talking about himself, clever,	bhB
16. not cricketers, dreamers, not believing that cricket is extinct,	ec'a'
17. simpletons, needing to push his own way in life, worth knowing.,	vGn
18. doubting whether we are a free nation, having heard of Magna Charta ,	kd
19. not worth knowing., believing that cricket is extinct, willing to walk rather than take a cab, not reading the papers,	Ear'G'
20. not studying Modern History , Wilson, not studying Ancient History,	w'z'F
21. not rich, not willing to walk rather than take a cab,	t'E'
22. doubting whether we are a free nation, thoughtful, reading the papers,	Cdr

The registry is:

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

and the barred premises are as follows:

1	barred by	6 10 17
2	barred by	9 13 20
3	barred by	14 22
7	barred by	1 12 14 18 22
12	barred by	1 9 15
18	barred by	2 8

Solution to be tested is FBb

This document was last updated 7 September 2020

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