The (almost really) Complete Works of Lewis Carroll

1. (1) There is always sunshine when the wind is in the East;
(2) When it is cold and foggy, my neighbour practises the flute;
(3) When my fire smokes, I set the door open;
(4) When it is cold and I feel rheumatic, I light my fire;
(5) When the wind is in the East and comes in gusts, my fire smokes;
(6) When I keep the door open, I am free from headache;
(7) Even when the sun is shining and it is not cold, I keep my window shut if it is foggy;
(8) When the wind does not come in gusts, and when I have a fire and keep the door shut, I do not feel rheumatic;
(9) Sunshine always brings on fog;
(10) When my neighbour practises the flute, I shut the door, even if I have no headache;
(11) When there is a fog and the wind is in the East, I feel rheumatic.
Prove that, when the wind is in the East, I keep my window shut.

2. A certain Railway-Company has appointed a Committee of Shareholders, under the following conditions:—Directors are ex-officio members of it; Bondholders also are admissible; all others are inadmissible.
It is given that:—
(1) All admissible Shareholders, who are on the Committee and are lame Directors, live in town;
(2) All short-sighted elderly Shareholders, who are admissible but are not Directors, are on the Committee;
(3) All elderly Shareholders, living out of town, who are neither Directors nor Members of the Committee, are admissible;
(4) All lame short-sighted Shareholders, who are admissible and are on the Committee, are Directors.
Prove that no lame elderly Shareholders, who live out of town, are short-sighted.

3. Prove that, if A is greater than B, and if B is greater than C, A is greater than C.

4. (1) All, whom I have taught, except any own sons, know something;
(2) A contented barber is a welcome visitor;
(3) All, except those who are in this house, are scholars;
(4) All the fat men, 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) Inattentive people 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 but the young 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 fat;
(16) All attentive scholars, who are not boys, are boastful;
(17) My brothers are all barbers;
(18) Any one, who wears a white apron and can endure a hurdy-gurdy, is worthy of respect;
(19) No boys dance jigs when at lessons;
(20) Those of my sons, who are always complaining, are ambitious;
(21) All the hard-reading men, who have been plucked, are fat;
(22) All respectable barbers dance jigs;
(23) Any one, who has a headache, is either attentive or else is one of my old pupils;
(24) Boastful persons do little;
(25) All the young, when not at lessons, like beating a gong;
(26) All, except scholars, make foolish remarks;
(27) Boys are mischievous;
(28) All my sons, except Peter, are candidates for Responsions;
(29) All grinning barbers are in good health;
(30) All, who are ambitious, read hard;
(31) A man in good spirits, who does not like beating a gong, cannot endure a hurdy-gurdy;
(32) All the candidates for Matriculation have been plucked;
(33) No boaster is a welcome visitor;
(34) All mischievous persons, except my sons, like toffy;
(35) Any one, who does not admire a bald head, is a barber;
(36) All invalids are fanciful.
Prove that no invalid with a headache can endure a hurdy-gurdy.

5. (1) One seldom finds a man who is neither a speculator nor bad to lend money to;
(2) All my friends, who are members of this club, are would-be celebrities;
(3) A wise man demands a receipt when he pays a bill;
(4) No handsome man, outside this town, is sure to get into hot water;
(5) No dancing-master is sought after, if very fat;
(6) No passionate man is popular, unless he is generous;
(7) A foolish speculator is on the road to ruin;
(8) A generous man gets testimonials, if he blows his own trumpet;
(9) All wise enthusiasts are poetical;
(10) A man, who dresses in sheep-skins and lives on whale-blubber, is an Arctic voyager;
(11) A generous man, who is not a dandy, retails other people’s jokes;
(12) A passionate man, who is above taking advice, is sure to get into hot water;
(13) An ugly man, who gets on badly, is not an eligible suitor;
(14) All foolish dandies are old;
(15) All British merchants are economical;
(16) A man, who has not dreamy eyes, is despised by ladies, unless he is intimate with the Royal Family;
(17) A man, who blows his own trumpet, is noticed by society;
(18) All wise noblemen are rich;
(19) A man does not demand receipts when he pays bills, unless he is getting on badly;
(20) All the firemen in this town are ugly;
(21) All uncommon men, who are not would-be celebrities, are members of this club;
(22) A man, who is noticed by society and gets testimonials, is no fool;
(23) No economical man is bad to lend money to, unless he lives on whale-blubber;
(24) No influential man is sought after, unless he is a dancing-master;
(25) Commoners are eligible suitors, if intimate with the Royal Family;
(26) All wise dreamy-eyed men are fond of barley-sugar;
(27) A man without enthusiasm loves walking by moonlight;
(28) An overbearing man is influential, if he is generous;
(29) Arctic voyagers, who dress in sheep-skins, are wise;
(30) No one is economical, unless he is a merchant;
(31) All would-be celebrities, who retail other people’s jokes, blow their own trumpets;
(32) All the wise men in this town are firemen;
(33) A man, who is despised by ladies, is sought after, provided he loves walking by moonlight;
(34) Old dandies retail other people’s jokes;
(35) Men, who pay no bills, get on badly;
(36) All foolish members of this club are friends of mine;
(37) No one, who is above taking advice, has influence if he is overbearing;
(38) A speculator, who is on the road to ruin, is a bad man to lend money to;
(39) Men with dreamy eyes, who are fond of barley-sugar, are despised by ladies;
(40) All wise dancing-masters are very fat;
(41) Rich noblemen are eligible suitors;
(42) All men, who live on whale-blubber and are above taking advice, dress in sheep-skins;
(43) All poetical enthusiasts love walking by moonlight;
(44) All foreign merchants are wise.
Prove that no passionate overbearing man is popular.