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."]
(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;
(7) John declines to go into Society, but never gives himself airs;
(8) Brothers, who are apt to be self-conscious, though not _both_ of them handsome, usually dislike Society;
(9) Men of the same height, who do not give themselves airs, are free from self-consciousness;
(10) Men, who agree on questions of Art, though they differ in Politics, and who are not both of them ugly, are always admired;
(11) Men, who hold opposite views about Art and are not admired, always give themselves airs;
(12) Brothers of the same height always differ in Politics;
(13) Two handsome men, who are neither both of them admired nor both of them self-conscious, are no doubt of different heights;
(14) Brothers, who are self-conscious, and do not both of them like Society, never look well when walking together.