As an interesting excursion befitting Bertrand Russell's comment about mathemat-ics, consider the following axiom system (adapted from Howard Eves, Survey of Geometry, Volume 1, p. 390).
Undefined terms: abbas, dabbas
AXIOMS:
(1) Every abba is a collection of at least two dabbas.
(2) There exist at least two dabbas.
(3) If d and d' are two dabbas, then there exists one and only one abba con-taining both d and d'.
(4) If a is an abba, then there exists a dabba d not in a.
(5) If a is an abba, and d is a dabba not in a, then there exists one and only one abba containing d and not containing any dabba that is in a.
(a) Deduce the following theorems from this postulate set:
(1) Every dabba is contained in at least two abbas.
(2) There exist at least four distinct dabbas.
(3) There exist at least six distinct abbas.
(b) Find two models for this postulate set, one having four dabbas and six abbas, and the other having nine dabbas, twelve abbas, and three dabbas on each abba.
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.