Complete Works of Lewis Carroll (205 page)

2.

(1) A logician, who eats pork-chops for supper, will probably lose money;

(2) A gambler, whose appetite is not ravenous, will probably lose money;

(3) A man who is depressed, having lost money and being likely to lose more, always rises at 5 a.m.;

(4) A man, who neither gambles nor eats pork-chops for supper, is sure to have a ravenous appetite;

(5) A lively man, who goes to bed before 4 a.m., had better take to cab-driving;

(6) A man with a ravenous appetite, who has not lost money and does not rise at 5 a.m., always eats pork-chops for supper;

(7) A logician, who is in danger of losing money, had better take to cab-driving;

(8) An earnest gambler, who is depressed though he has not lost money, is in no danger of losing any;

(9) A man, who does not gamble, and whose appetite is not ravenous, is always lively;

(10) A lively logician, who is really in earnest, is in no danger of losing money;

(11) A man with a ravenous appetite has no need to take to cab-driving, if he is really in earnest;

(12) A gambler, who is depressed though in no danger of losing money, sits up till 4 a.m.

(13) A man, who has lost money and does not eat pork-chops for supper, had better take to cab-driving, unless he gets up at 5 a.m.

(14) A gambler, who goes to bed before 4 a.m., need not take to cab-driving, unless he has a ravenous appetite;

(15) A man with a ravenous appetite, who is depressed though in no danger of losing, is a gambler.

Univ.
“men”;
a
 = earnest;
b
 = eating pork-chops for supper;
c
 = gamblers;
d
 = getting up at 5;
e
 = having lost money;
h
 = having a ravenous appetite;
k
 = likely to lose money;
l
 = lively;
m
 = logicians;
n
 = men who had better take to cab-driving;
r
 = sitting up till 4.

[N.B.
In this Problem, clauses, beginning with “though”, are intended to be treated as
essential
parts of the Propositions in which they occur, just as if they had begun with “and”.]

3.

(1) When the day is fine, I tell Froggy “You’re quite the dandy, old chap!”;

(2) Whenever I let Froggy forget that £10 he owes me, and he begins to strut about like a peacock, his mother declares “He shall
not
go out a-wooing!”;

(3) Now that Froggy’s hair is out of curl, he has put away his gorgeous waistcoat;

(4) Whenever I go out on the roof to enjoy a quiet cigar, I’m sure to discover that my purse is empty;

(5) When my tailor calls with his little bill, and I remind Froggy of that £10 he owes me, he does
not
grin like a hyæna;

(6) When it is very hot, the thermometer is high;

(7) When the day is fine, and I’m not in the humour for a cigar, and Froggy is grinning like a hyæna, I never venture to hint that he’s quite the dandy;

(8) When my tailor calls with his little bill and finds me with an empty purse, I remind Froggy of that £10 he owes me;

(9) My railway-shares are going up like anything!

(10) When my purse is empty, and when, noticing that Froggy has got his gorgeous waistcoat on, I venture to remind him of that £10 he owes me, things are apt to get rather warm;

(11) Now that it looks like rain, and Froggy is grinning like a hyæna, I can do without my cigar;

(12) When the thermometer is high, you need not trouble yourself to take an umbrella;

(13) When Froggy has his gorgeous waistcoat on, but is
not
strutting about like a peacock, I betake myself to a quiet cigar;

(14) When I tell Froggy that he’s quite the dandy, he grins like a hyæna;

(15) When my purse is tolerably full, and Froggy’s hair is one mass of curls, and when he is
not
strutting about like a peacock, I go out on the roof;

(16) When my railway-shares are going up, and when it is chilly and looks like rain, I have a quiet cigar;

(17) When Froggy’s mother lets him go a-wooing, he seems nearly mad with joy, and puts on a waistcoat that is gorgeous beyond words;

(18) When it is going to rain, and I am having a quiet cigar, and Froggy is
not
intending to go a-wooing, you had better take an umbrella;

(19) When my railway-shares are going up, and Froggy seems nearly mad with joy,
that
is the time my tailor always chooses for calling with his little bill;

(20) When the day is cool and the thermometer low, and I say nothing to Froggy about his being quite the dandy, and there’s not the ghost of a grin on his face, I haven’t the heart for my cigar!

4.

(1) Any one, fit to be an M.P., who is not always speaking, is a public benefactor;

(2) Clear-headed people, who express themselves well, have had a good education;

(3) A woman, who deserves praise, is one who can keep a secret;

(4) People, who benefit the public, but do not use their influence for good purpose, are not fit to go into Parliament;

(5) People, who are worth their weight in gold and who deserve praise, are always unassuming;

(6) Public benefactors, who use their influence for good objects, deserve praise;

(7) People, who are unpopular and not worth their weight in gold, never can keep a secret;

(8) People, who can talk for ever and are fit to be Members of Parliament, deserve praise;

(9) Any one, who can keep a secret and who is unassuming, is a never-to-be-forgotten public benefactor;

(10) A woman, who benefits the public, is always popular;

(11) People, who are worth their weight in gold, who never leave off talking, and whom it is impossible to forget, are just the people whose photographs are in all the shop-windows;

(12) An ill-educated woman, who is not clear-headed, is not fit to go into Parliament;

(13) Any one, who can keep a secret and is not for ever talking, is sure to be unpopular;

(14) A clear-headed person, who has influence and uses it for good objects, is a public benefactor;

(15) A public benefactor, who is unassuming, is not the sort of person whose photograph is in every shop-window;

(16) People, who can keep a secret and who use their influence for good purposes, are worth their weight in gold;

(17) A person, who has no power of expression and who cannot influence others, is certainly not a
woman
;

(18) People, who are popular and worthy of praise, either are public benefactors or else are unassuming.

Univ.
“persons”;
a
 = able to keep a secret;
b
 = clear-headed;
c
 = constantly talking;
d
 = deserving praise;
e
 = exhibited in shop-windows;
h
 = expressing oneself well;
k
 = fit to be an M.P.;
l
 = influential;
m
 = never-to-be-forgotten;
n
 = popular;
r
 = public benefactors;
s
 = unassuming;
t
 = using one’s influence for good objects;
v
 = well-educated;
w
 = women;
z
 = worth one’s weight in gold.

5.

Six friends, and their six wives, are staying in the same hotel; and they all walk out daily, in parties of various size and composition.
To ensure variety in these daily walks, they have agree to observe the following Rules:—

(1) If Acres is with (i.e.
is in the same party with) his wife, and Barry with his, and Eden with Mrs.
Hall, Cole must be with Mrs.
Dix;

(2) If Acres is with his wife, and Hall with his, and Barry with Mrs.
Cole, Dix must
not
be with Mrs.
Eden;

(3) If Cole and Dix and their wives are all in the same party, and Acres
not
with Mrs.
Barry, Eden must
not
be with Mrs.
Hall;

(4) If Acres is with his wife, and Dix with his, and Barry
not
with Mrs.
Cole, Eden must be with Mrs.
Hall;

(5) If Eden is with his wife, and Hall with his, and Cole with Mrs.
Dix, Acres must
not
be with Mrs.
Barry;

(6) If Barry and Cole and their wives are all in the same party, and Eden
not
with Mrs.
Hall, Dix must be with Mrs.
Eden.

The Problem is to prove that there must be, every day, at least
one
married couple who are not in the same party.

6.

After the six friends, named in Problem 5, had returned from their tour, three of them, Barry, Cole, and Dix, agreed, with two other friends of theirs, Lang and Mill, that the five should meet, every day, at a certain
table d’hôte
.
Remembering how much amusement they had derived from their code of rules for walking-parties, they devised the following rules to be observed whenever beef appeared on the table:—

(1) If Barry takes salt, then either Cole or Lang takes
one
only of the two condiments, salt and mustard: if he takes mustard, then either Dix takes neither condiment, or Mill takes both.

(2) If Cole takes salt, then either Barry takes only
one
condiment, or Mill takes neither: if he takes mustard, then either Dix or Lang takes both.

(3) If Dix takes salt, then either Barry takes neither condiment or Cole take both: if he takes mustard, then either Lang or Mill takes neither.

(4) If Lang takes salt, then Barry or Dix takes only
one
condiment: if he takes mustard, then either Cole or Mill takes neither.

(5) If Mill takes salt, then either Barry or Lang takes both condiments: if he takes mustard, then either Cole or Dix takes only
one
.

The Problem is to discover whether these rules are
compatible
; and, if so, what arrangements are possible.

[N.B.
In this Problem, it is assumed that the phrase “if Barry takes salt” allows of
two
possible cases, viz.
(1) “he takes salt
only
”; (2) “he takes
both
condiments”.
And so with all similar phrases.

It is also assumed that the phrase “either Cole or Lang takes
one
only of the two condiments” allows
three
possible cases, viz.
(1) “Cole takes
one
only, Lang takes both or neither”; (2) “Cole takes both or neither, Lang takes
one
only”; (3) “Cole takes
one
only, Lang takes
one
only”.
And so with all similar phrases.

It is also assumed that every rule is to be understood as implying the words “and
vice versâ
.”
Thus the first rule would imply the addition “and, if either Cole or Lang takes only
one
condiment, then Barry takes salt.”]

7.

(1) Brothers, who are much admired, are apt to be self-conscious;

(2) When two men of the same height are on opposite sides in Politics, if one of them has his admirers, so also has the other;

(3) Brothers, who avoid general Society, look well when walking together;

(4) Whenever you find two men, who differ in Politics and in their views of Society, and who are not both of them ugly, you may be sure that they look well when walking together;

(5) Ugly men, who look well when walking together, are not both of them free from self-consciousness;

(6) Brothers, who differs in Politics, and are not both of them handsome, never give themselves airs;