97:@0.942817:0.963886:0.964167:0.963886:0.964167:0.945448:0.942817:0.945448:0.000000:0.000000
Relaciones binarias: reflexiva, simétrica y transitiva:@0.095800:0.136254:0.626472:0.136254:0.626472:0.114445:0.095800:0.114445:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo1:@0.095800:0.177121:0.161754:0.177121:0.161754:0.162008:0.095800:0.162008:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dado el conjunto M = {1, 2, 4, 8} considerando que se establece la relación R de M :@0.095800:0.201159:0.698200:0.201159:0.698200:0.185490:0.095800:0.185490:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en M definida por “  divide a ”, ¿qué pares ordenados definen esta relación y qué :@0.095800:0.217756:0.698185:0.217756:0.698185:0.202086:0.095800:0.202086:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.235863:0.217756:0.243326:0.217756:0.243326:0.201394:0.235863:0.201394:0.000000
 y:@0.305573:0.217756:0.316703:0.217756:0.316703:0.201394:0.305573:0.201394:0.000000:0.000000
propiedad se aplica?:@0.095800:0.234352:0.246170:0.234352:0.246170:0.218682:0.095800:0.218682:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Solución:@0.095800:0.252690:0.156461:0.252690:0.156461:0.237577:0.095800:0.237577:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Encontramos la relación \x divide a y\:@0.095800:0.276728:0.368601:0.276728:0.368601:0.261058:0.095800:0.261058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a) :@0.124289:0.300447:0.143529:0.300447:0.143529:0.283311:0.124289:0.283311:0.000000:0.000000:0.000000
1 divide a 1, 2, 4, y 8 :@0.152779:0.300447:0.301140:0.300447:0.301140:0.284777:0.152779:0.284777:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c):@0.412406:0.300447:0.426503:0.300447:0.426503:0.283311:0.412406:0.283311:0.000000:0.000000
   4 divide a 4 y 8 :@0.426503:0.300447:0.551295:0.300447:0.551295:0.284777:0.426503:0.284777:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b)   :@0.124272:0.324166:0.152098:0.324166:0.152098:0.307030:0.124272:0.307030:0.000000:0.000000:0.000000:0.000000:0.000000
2 divide a 2, 4, y 8 :@0.152098:0.324166:0.284224:0.324166:0.284224:0.308496:0.152098:0.308496:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d)  :@0.412406:0.324166:0.436620:0.324166:0.436620:0.307030:0.412406:0.307030:0.000000:0.000000:0.000000:0.000000
 8 divide a 8 :@0.436620:0.324166:0.528169:0.324166:0.528169:0.308496:0.436620:0.308496:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los pares ordenados que definen la relación son::@0.095782:0.347885:0.452685:0.347885:0.452685:0.332215:0.095782:0.332215:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R = {(1, 1); (1, 2); (1, 4); (1, 8); (2, 2); (2, 4); (2, 8); (4, 4); (4, 8); (8, 8)}:@0.095782:0.371604:0.549028:0.371604:0.549028:0.355934:0.095782:0.355934:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Como podemos observar, se cumple la :@0.095782:0.395323:0.386271:0.395323:0.386271:0.379653:0.095782:0.379653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
propiedad reflexiva:@0.386271:0.395323:0.541430:0.395323:0.541430:0.378422:0.386271:0.378422:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.541430:0.395323:0.544637:0.395323:0.544637:0.379653:0.541430:0.379653:0.000000
Ejemplo 2:@0.095800:0.427944:0.165306:0.427944:0.165306:0.412831:0.095800:0.412831:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dado el conjunto Q = {Teresa, Martha, Ana} considerando que se establece  :@0.095800:0.451982:0.698181:0.451982:0.698181:0.436312:0.095800:0.436312:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la relación R de Q en Q definida por “ es hermana de  ”, ¿cómo relacionamos :@0.095800:0.468578:0.698170:0.468578:0.698170:0.452909:0.095800:0.452909:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.386317:0.468578:0.397098:0.468578:0.397098:0.452217:0.386317:0.452217:0.000000:0.000000
y:@0.519745:0.468578:0.527226:0.468578:0.527226:0.452217:0.519745:0.452217:0.000000
 :@0.533528:0.468264:0.537079:0.468264:0.537079:0.453151:0.533528:0.453151:0.000000
 :@0.694135:0.468578:0.698170:0.468578:0.698170:0.452909:0.694135:0.452909:0.000000
el problema?:@0.095789:0.485175:0.191374:0.485175:0.191374:0.469505:0.095789:0.469505:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Solución:@0.095800:0.503513:0.156461:0.503513:0.156461:0.488400:0.095800:0.488400:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a) :@0.124292:0.527551:0.143530:0.527551:0.143530:0.510415:0.124292:0.510415:0.000000:0.000000:0.000000
T es hermana de M :@0.152781:0.527551:0.296719:0.527551:0.296719:0.511881:0.152781:0.511881:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d):@0.413956:0.527551:0.430725:0.527551:0.430725:0.510415:0.413956:0.510415:0.000000:0.000000
  A es hermana de T:@0.430725:0.527551:0.578017:0.527551:0.578017:0.511881:0.430725:0.511881:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b) :@0.124273:0.551270:0.144654:0.551270:0.144654:0.534134:0.124273:0.534134:0.000000:0.000000:0.000000
M es hermana de T :@0.152763:0.551270:0.295927:0.551270:0.295927:0.535600:0.152763:0.535600:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
e):@0.413937:0.551270:0.429454:0.551270:0.429454:0.534134:0.413937:0.534134:0.000000:0.000000
  M es hermana de A:@0.429454:0.551270:0.584541:0.551270:0.584541:0.535600:0.429454:0.535600:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c) :@0.124255:0.574989:0.142075:0.574989:0.142075:0.557853:0.124255:0.557853:0.000000:0.000000:0.000000
T es hermana de A :@0.152744:0.574989:0.293126:0.574989:0.293126:0.559319:0.152744:0.559319:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f):@0.413919:0.574989:0.427316:0.574989:0.427316:0.557853:0.413919:0.557853:0.000000:0.000000
  A es hermana de M:@0.427316:0.574989:0.584522:0.574989:0.584522:0.559319:0.427316:0.559319:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los pares ordenados que definen esta relación son::@0.095747:0.598708:0.470249:0.598708:0.470249:0.583038:0.095747:0.583038:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R = { (T, M); (M, T); (T, A); (A, T); (M, A); (A, M) }:@0.095747:0.622427:0.416716:0.622427:0.416716:0.606757:0.095747:0.606757:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Se cumple la :@0.095747:0.646146:0.193819:0.646146:0.193819:0.630476:0.095747:0.630476:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
propiedad simétrica:@0.193819:0.646146:0.353900:0.646146:0.353900:0.629245:0.193819:0.629245:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.353900:0.646146:0.357107:0.646146:0.357107:0.630476:0.353900:0.630476:0.000000
Ejemplo 3:@0.095800:0.678767:0.165306:0.678767:0.165306:0.663654:0.095800:0.663654:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dado el conjunto S = {5, 6, 7, 8}, se establece la relación R de S en S definida por :@0.095800:0.702805:0.698237:0.702805:0.698237:0.687135:0.095800:0.687135:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.694146:0.702805:0.698181:0.702805:0.698181:0.687135:0.694146:0.687135:0.000000
“  es mayor que  ”. ¿Cómo verificamos la propiedad transitiva?:@0.095800:0.719401:0.547991:0.719401:0.547991:0.703731:0.095800:0.703731:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.101200:0.719401:0.108663:0.719401:0.108663:0.703040:0.101200:0.703040:0.000000
y:@0.215891:0.719401:0.223373:0.719401:0.223373:0.703040:0.215891:0.703040:0.000000
Solución:@0.095800:0.737739:0.156461:0.737739:0.156461:0.722626:0.095800:0.722626:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a) :@0.124292:0.761777:0.143530:0.761777:0.143530:0.744642:0.124292:0.744642:0.000000:0.000000:0.000000
6 es mayor que 5:@0.152781:0.761777:0.277995:0.761777:0.277995:0.746108:0.152781:0.746108:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b) :@0.124292:0.785496:0.144673:0.785496:0.144673:0.768361:0.124292:0.768361:0.000000:0.000000:0.000000
7 es mayor que 5, 6:@0.152781:0.785496:0.294232:0.785496:0.294232:0.769827:0.152781:0.769827:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c) :@0.124292:0.809215:0.142111:0.809215:0.142111:0.792080:0.124292:0.792080:0.000000:0.000000:0.000000
8 es mayor que 5, 6, 7:@0.152781:0.809215:0.310466:0.809215:0.310466:0.793546:0.152781:0.793546:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los pares ordenados que definen esta relación son::@0.095803:0.832934:0.470304:0.832934:0.470304:0.817265:0.095803:0.817265:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R = { (6, 5); (7, 5); (7, 6); (8, 5); (8, 6); (8, 7) }:@0.095803:0.856653:0.388176:0.856653:0.388176:0.840983:0.095803:0.840983:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La relación cumple la :@0.095803:0.880372:0.255147:0.880372:0.255147:0.864702:0.095803:0.864702:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
propiedad transitiva:@0.255147:0.880372:0.417271:0.880372:0.417271:0.863472:0.255147:0.863472:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. :@0.417271:0.880372:0.424513:0.880372:0.424513:0.864702:0.417271:0.864702:0.000000:0.000000
R es transitiva si un elemento está relacionado con un segundo y este con un :@0.095803:0.904091:0.698200:0.904091:0.698200:0.888421:0.095803:0.888421:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tercero, y si el primero está relacionado con el tercero.:@0.095803:0.920688:0.489098:0.920688:0.489098:0.905018:0.095803:0.905018:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Las relaciones :@0.732565:0.165815:0.828539:0.165815:0.828539:0.151570:0.732565:0.151570:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
binarias pueden :@0.732565:0.180903:0.844136:0.180903:0.844136:0.166658:0.732565:0.166658:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cumplir las siguientes :@0.732565:0.195991:0.880118:0.195991:0.880118:0.181745:0.732565:0.181745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
propiedades, pero no :@0.732565:0.211078:0.879230:0.211078:0.879230:0.196833:0.732565:0.196833:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
necesariamente todas. :@0.732565:0.226166:0.886332:0.226166:0.886332:0.211921:0.732565:0.211921:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Propiedad reflexiva:@0.732565:0.248382:0.872982:0.248382:0.872982:0.233018:0.732565:0.233018:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.872982:0.248382:0.876366:0.248382:0.876366:0.232804:0.872982:0.232804:0.000000
Los elementos del :@0.732565:0.270599:0.857603:0.270599:0.857603:0.256354:0.732565:0.256354:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
conjunto están :@0.732565:0.285686:0.836848:0.285686:0.836848:0.271441:0.732565:0.271441:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
relacionados entre sí :@0.732565:0.300774:0.873266:0.300774:0.873266:0.286529:0.732565:0.286529:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de tal manera que: para :@0.732565:0.315862:0.893874:0.315862:0.893874:0.301616:0.732565:0.301616:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
todo elemento  de A, :@0.732565:0.330949:0.883619:0.330949:0.883619:0.316704:0.732565:0.316704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.836528:0.330949:0.846329:0.330949:0.846329:0.316075:0.836528:0.316075:0.000000:0.000000
entonces   :@0.732565:0.346037:0.816895:0.346036:0.816895:0.331790:0.732565:0.331792:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x x:@0.816895:0.346036:0.847451:0.346036:0.847451:0.330910:0.816895:0.330910:0.000000:0.000000:0.000000
   :@0.824282:0.346036:0.840063:0.346036:0.840063:0.330458:0.824282:0.330458:0.000000:0.000000:0.000000
R:@0.827666:0.346036:0.836679:0.346036:0.836679:0.330923:0.827666:0.330923:0.000000
.:@0.847451:0.346036:0.850366:0.346036:0.850366:0.331790:0.847451:0.331790:0.000000
∀ ∈:@0.732563:0.368780:0.771814:0.368780:0.771814:0.352775:0.732563:0.352775:0.000000:0.000000:0.000000
     A,  R  .:@0.743737:0.368252:0.823495:0.368252:0.823495:0.354007:0.743737:0.354007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.747406:0.368252:0.754190:0.368252:0.754190:0.353378:0.747406:0.353378:0.000000
x  x:@0.791867:0.368252:0.820580:0.368252:0.820580:0.353378:0.791867:0.353378:0.000000:0.000000:0.000000:0.000000
Propiedad simétrica:@0.732563:0.390469:0.877455:0.390469:0.877455:0.375104:0.732563:0.375104:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.877455:0.390469:0.880839:0.390469:0.880839:0.374891:0.877455:0.374891:0.000000
Si dos elementos de un :@0.732563:0.412685:0.892430:0.412685:0.892430:0.398440:0.732563:0.398440:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
conjunto cumplen que, :@0.732563:0.427773:0.893215:0.427773:0.893215:0.413528:0.732563:0.413528:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
si el primer elemento :@0.732563:0.442860:0.877870:0.442860:0.877870:0.428615:0.732563:0.428615:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
está relacionado con :@0.732563:0.457948:0.874623:0.457948:0.874623:0.443703:0.732563:0.443703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el segundo, entonces :@0.732563:0.473036:0.879162:0.473036:0.879162:0.458790:0.732563:0.458790:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se cumple también :@0.732563:0.488123:0.865309:0.488123:0.865309:0.473878:0.732563:0.473878:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que el segundo está :@0.732563:0.503211:0.871558:0.503211:0.871558:0.488966:0.732563:0.488966:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
relacionado con el :@0.732563:0.518298:0.859144:0.518298:0.859144:0.504053:0.732563:0.504053:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
primero: :@0.732563:0.533386:0.792468:0.533386:0.792468:0.519141:0.732563:0.519141:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
si:@0.732563:0.555603:0.742313:0.555603:0.742313:0.541357:0.732563:0.541357:0.000000:0.000000
 :@0.742313:0.555603:0.745697:0.555603:0.745697:0.540025:0.742313:0.540025:0.000000
x y:@0.745697:0.555603:0.775952:0.555603:0.775952:0.540477:0.745697:0.540477:0.000000:0.000000:0.000000
 :@0.753085:0.555603:0.756167:0.555603:0.756167:0.540050:0.753085:0.540050:0.000000
R:@0.756167:0.555603:0.765180:0.555603:0.765180:0.540490:0.756167:0.540490:0.000000
 :@0.765180:0.555603:0.768564:0.555603:0.768564:0.540025:0.765180:0.540025:0.000000
   :@0.775952:0.555603:0.798366:0.555599:0.798366:0.541354:0.775952:0.541357:0.000000:0.000000:0.000000
y x:@0.798366:0.555599:0.828923:0.555599:0.828923:0.540473:0.798366:0.540473:0.000000:0.000000:0.000000
    .:@0.805754:0.555599:0.833278:0.555599:0.833278:0.540021:0.805754:0.540021:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.809138:0.555599:0.818151:0.555599:0.818151:0.540486:0.809138:0.540486:0.000000
∀:@0.732563:0.578343:0.743737:0.578343:0.743737:0.562338:0.732563:0.562338:0.000000
  ,     A,  R   :@0.743569:0.577815:0.834803:0.577815:0.834803:0.563570:0.743569:0.563570:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.747071:0.577815:0.766738:0.577815:0.766738:0.562941:0.747071:0.562941:0.000000:0.000000:0.000000
∈:@0.770072:0.578343:0.784026:0.578343:0.784026:0.562338:0.770072:0.562338:0.000000
x  y:@0.803241:0.577815:0.831302:0.577815:0.831302:0.562941:0.803241:0.562941:0.000000:0.000000:0.000000:0.000000
  R  .:@0.856246:0.577814:0.890555:0.577814:0.890555:0.563569:0.856246:0.563569:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y  x:@0.859747:0.577814:0.887808:0.577814:0.887808:0.562940:0.859747:0.562940:0.000000:0.000000:0.000000:0.000000
Propiedad transitiva:@0.732563:0.600031:0.879312:0.600031:0.879312:0.584666:0.732563:0.584666:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dados tres elementos :@0.732563:0.622247:0.881455:0.622247:0.881455:0.608002:0.732563:0.608002:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
del conjunto, si el :@0.732563:0.637335:0.852877:0.637335:0.852877:0.623089:0.732563:0.623089:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
primer elemento está :@0.732563:0.652422:0.879932:0.652422:0.879932:0.638177:0.732563:0.638177:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
relacionado con el :@0.732563:0.667510:0.859144:0.667510:0.859144:0.653265:0.732563:0.653265:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
segundo, y el segundo :@0.732563:0.682598:0.887672:0.682598:0.887672:0.668352:0.732563:0.668352:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
está relacionado con :@0.732563:0.697685:0.874623:0.697685:0.874623:0.683440:0.732563:0.683440:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el tercero, entonces, :@0.732563:0.712773:0.869730:0.712773:0.869730:0.698528:0.732563:0.698528:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el primero está :@0.732563:0.727860:0.835723:0.727860:0.835723:0.713615:0.732563:0.713615:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
relacionado con el :@0.732563:0.742948:0.859144:0.742948:0.859144:0.728703:0.732563:0.728703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tercero: :@0.732563:0.758036:0.786372:0.758036:0.786372:0.743790:0.732563:0.743790:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
si :@0.732563:0.780252:0.745982:0.780252:0.745982:0.766007:0.732563:0.766007:0.000000:0.000000:0.000000
x y y z:@0.745982:0.780252:0.821384:0.780252:0.821384:0.765127:0.745982:0.765127:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.753370:0.780252:0.756452:0.780252:0.756452:0.764699:0.753370:0.764699:0.000000
R e  R:@0.756452:0.780252:0.811350:0.780252:0.811350:0.765139:0.756452:0.765139:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
     :@0.765465:0.780252:0.791397:0.780252:0.791397:0.764674:0.765465:0.764674:0.000000:0.000000:0.000000:0.000000:0.000000
       :@0.811350:0.780252:0.853097:0.780250:0.853097:0.764697:0.811350:0.764699:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x z:@0.842626:0.780250:0.872446:0.780250:0.872446:0.765124:0.842626:0.765124:0.000000:0.000000:0.000000
R:@0.853097:0.780250:0.862109:0.780250:0.862109:0.765137:0.853097:0.765137:0.000000
 :@0.862109:0.780250:0.865493:0.780250:0.865493:0.764672:0.862109:0.764672:0.000000
∀:@0.732563:0.802994:0.743737:0.802994:0.743737:0.786989:0.732563:0.786989:0.000000
  ,  ,     A,  R  ):@0.743737:0.802466:0.856028:0.802466:0.856028:0.788221:0.743737:0.788221:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y z:@0.747406:0.802466:0.780743:0.802466:0.780743:0.787592:0.747406:0.787592:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.784412:0.802994:0.798366:0.802994:0.798366:0.786989:0.784412:0.786989:0.000000
(x  y    :@0.818419:0.802466:0.873771:0.802465:0.873771:0.787591:0.818419:0.787592:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.873771:0.802465:0.877439:0.802465:0.877439:0.788220:0.873771:0.788220:0.000000
( R  ):@0.732565:0.817552:0.769973:0.817552:0.769973:0.803307:0.732565:0.803307:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y  z  :@0.737004:0.817552:0.772988:0.817552:0.772988:0.802679:0.737004:0.802679:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 x  z:@0.794766:0.817552:0.826294:0.817552:0.826294:0.802679:0.794766:0.802679:0.000000:0.000000:0.000000:0.000000:0.000000
R  .:@0.807582:0.817552:0.829209:0.817552:0.829209:0.803307:0.807582:0.803307:0.000000:0.000000:0.000000:0.000000
¿Sabías que?:@0.765136:0.141306:0.867004:0.141306:0.867004:0.124405:0.765136:0.124405:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000
maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000
®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000