Examples. Sets of Premisses
1. (1) If all a are b, no c are d;
(2) If some a are not b, some c are not d.
Prove that, if all c are d, no a are b.
2. (1) If some a are b and some not, some c are not d;
(2) If some c are d, either some a are b, or some e are not f.
Prove that, if all c are d, and if all e are f, all a are b.
3. (1) If all a are b, no c are d;
(2) If no a are b, and if some c are not d, some e are not f;
(3) If some a are b and some not, and if some g are h, no e are f.
Prove that, if some c are d and some not, and if all e are f, no g are h.
4. (1) If some a are b and some not, some c are not d;
(2) If some e are f, and if some g are h, some k are l;
(3) If all m are n, no p are q;
(4) If some c are d and some not, some g are h;
(5) If no e are f, and if some p are q, some k are not l;
(6) If some e are not f, and if some g are not h, some p are q;
(7) If some c are not d, and if some k are l, no e are f;
(8) If some g are not h, and if some k are not l, some m are n;
(9) If some e are not f, and if some p are q, some a are not b;
(10) If some a are b, and if some c are d, some g are not h;
(11) If some c are not d, and if some m are not n, some e are f.
Prove that, if some a are b, and if some e are not f, no c are d.
5. (1) If all a are b, and if some e are f and some not, some c are d;
(2) If all e are f, and if some g are h, some a are not b;
(3) If some c are d and some not, and if some e are not f, no a are b;
(4) If some a are not b, and if some e are f, no g are h;
(5) If some c are d, and if some g are h, some c are not d.
Prove that, if some a are b, and if all g are h, no e are f.
6. Six friends, A, B, C, D, E, F, and their six wives, all walk out daily, in parties of various size and composition, under the following conditions:—
(1) When A is with (i. e. is in the same party with) his wife, and B with his, and E with F’s, C is with D’s;
(2) When A is with his wife, and F with his, and when B is with C’s wife, D is not with E’s;
(3) When C and D and their wives are in the same party, and when A is not with B’s wife, E is not with F’s;
(4) When A is with his wife, and D with his, and when B is not with C’s, E is with F’s;
(5) When E is with his wife, and F with his, and C with D’s, A is not with B’s;
(6) When B and C and their wives are in the same party, and when E is not with F’s wife, D is with E’s.
Prove that there is, every day, at least one couple who are not in the same party.
7. (1) All active old Jews are healthy;
(2) All indolent magistrates are unpopular;
(3) All rich snuff-takers are unhealthy;
(4) All unpopular magistrates are Jews;
(5) All young snuff-takers are poor;
(6) All rich old men, who are unhealthy, are unpopular;
(7) All magistrates, who are not Jews, are studious;
(8) All rich magistrates are talented;
(9) All talented and popular students are rich;
(10) All poor snuff-takers are unpopular;
(11) All unpopular magistrates abstain from snuff;
(12) All talented Jews, who are active, are rich.
Prove that no magistrates take snuff.
[Dec. 1892.]