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Help from the fourth postulate to the seventh postulate.
HOMEWORK N°1 NAME: 1.Show that the seven postulates are true in the three proposed models. POSTULATES OF SYSTEM 73 * Postulate 1 If p, q EP, pq, there exists at least one À E A such that p EA and q EX. * Postulate 2 If p, q E P and p #q, there is at most one element of A such that p E A and q E A. * Postulate 3 If A μEA, A#p, there exists at least one element p of P such that p EA and p = μ. * Postulate 4 The set A is not zero. * Postulate 5 If A E A, there exist at least three elements p, q, r of P (p‡q‡r #p) such that p, q, r X. * Postulate 6 If A E A, there exists p E P such that p #A * Postulate 7 If A E A, there are at most three distinct pairwise elements of P that are elements of A.

Model 1 A model of the system is obtained by the following interpretations: the set P of points is the set of seven letters A, B, C, D, E, F, G; and the set A of lines consists of those subsets of P that form the columns of the array. A B C B C 1 DE Model 2. D E F G G A B B C. DEF F G A 45 Figure 5

3 N 0 Figure 6 5 Model 3