(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;