(2) Whenever some of the Scotch are dancing reels, and some of the Irish fighting, some of the Welsh are eating toasted cheese; (3) Whenever all the Germans are playing chess, some of the Eleven are _not_ oiling their bats; (4) Whenever some of the Monitors are asleep, and some not, some of the Irish are fighting; (5) Whenever some of the Germans are playing chess, and none of the Scotch are dancing reels, some of the Welsh are _not_ eating toasted cheese; (6) Whenever some of the Scotch are _not_ dancing reels, and some of the Irish _not_ fighting, some of the Germans are playing chess; (7) Whenever some of the Monitors are awake, and some of the Welsh are eating toasted cheese, none of the Scotch are dancing reels; (8) Whenever some of the Germans are _not_ playing chess, and some of the Welsh are _not_ eating toasted cheese, none of the Irish are fighting; pg187 (9) Whenever all the English are singing "Rule Britannia," and some of the Scotch are _not_ dancing reels, none of the Germans are playing chess; (10) Whenever some of the English are singing "Rule Britannia", and some of the Monitors are asleep, some of the Irish are _not_ fighting; (11) Whenever some of the Monitors are awake, and some of the Eleven are _not_ oiling their bats, some of the Scotch are dancing reels; (12) Whenever some of the English are singing "Rule Britannia", and some of the Scotch are _not_ dancing reels, * * * * Here the MS. breaks off suddenly. The Problem is to complete the sentence, if possible. [N.B. In solving this Problem, it is necessary to remember that the Proposition "All x are y" is a _Double_ Proposition, and is equivalent to "Some x are y, and none are y'." See p. 17.] 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; pg188 (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.