213:@0.937671:0.974518:0.968375:0.974518:0.968375:0.956333:0.937671:0.956333:0.000000:0.000000:0.000000
Pensamiento espacial:@0.721207:0.043660:0.914624:0.043660:0.914624:0.024915:0.721207:0.024915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dos proposiciones unidas por las palabras “y”   y   “o”, forman una proposición compuesta.:@0.085923:0.143414:0.727749:0.143414:0.727749:0.127701:0.085923:0.127701:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si se unen con la palabra “y”, se llama conjunción y se representa :@0.082576:0.163628:0.551125:0.163628:0.551125:0.147916:0.082576:0.147916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p  q:@0.550635:0.163628:0.590196:0.163628:0.590196:0.147222:0.550635:0.147222:0.000000:0.000000:0.000000:0.000000
⋀:@0.563079:0.164211:0.578412:0.164211:0.578412:0.146557:0.563079:0.146557:0.000000
 :@0.578308:0.157904:0.580991:0.157904:0.580991:0.147612:0.578308:0.147612:0.000000
Si se unen con la palabra “o”, se llama disyunción y se representa :@0.082579:0.183848:0.547116:0.183848:0.547116:0.168135:0.082579:0.168135:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p   q:@0.546626:0.183848:0.586809:0.183848:0.586809:0.167442:0.546626:0.167442:0.000000:0.000000:0.000000:0.000000:0.000000
⋁:@0.559069:0.184431:0.574403:0.184431:0.574403:0.166776:0.559069:0.166776:0.000000
La negación de una proposición es una nueva proposición con significado opuesto y valor de verdad opuesto. :@0.082598:0.204068:0.920124:0.204068:0.920124:0.188355:0.082598:0.188355:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.915949:0.204068:0.919980:0.204068:0.919980:0.188355:0.915949:0.188355:0.000000
Se representa :@0.082598:0.220710:0.185419:0.220710:0.185419:0.204997:0.082598:0.204997:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∙:@0.185273:0.221292:0.200606:0.221292:0.200606:0.203638:0.185273:0.203638:0.000000
p:@0.200514:0.220710:0.209773:0.220710:0.209773:0.204304:0.200514:0.204304:0.000000
Ejemplo 3:@0.073118:0.278180:0.149489:0.278180:0.149489:0.261510:0.073118:0.261510:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Da un contraejemplo que invalide la afirmación “todos los triángulos tienen tres ángulos agudos”. Basta con citar un :@0.073118:0.309120:0.930728:0.309120:0.930728:0.293407:0.073118:0.293407:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
triángulo rectángulo, que posee un ángulo recto, para invalidar la afirmación. :@0.073118:0.325761:0.634118:0.325761:0.634118:0.310049:0.073118:0.310049:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3.2 Razonamiento deductivo:@0.085922:0.360361:0.303397:0.360361:0.303397:0.343692:0.085922:0.343692:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.  Identifica las condiciones dadas: a esto se le llama hipótesis.:@0.082576:0.380577:0.543595:0.380577:0.543595:0.364865:0.082576:0.364865:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.  Identifica la tesis: es lo que se desea demostrar.:@0.082576:0.400792:0.451421:0.400792:0.451421:0.385079:0.082576:0.385079:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3.  Utiliza los axiomas y los teoremas ya demostrados para seguir un razonamiento lógico que conlleve a la :@0.082576:0.421008:0.919687:0.421008:0.919687:0.405295:0.082576:0.405295:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
demostración o negación de la tesis.:@0.112704:0.437650:0.377091:0.437650:0.377091:0.421937:0.112704:0.421937:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4.  Redacta la conclusión del procedimiento.:@0.084249:0.457866:0.414176:0.457866:0.414176:0.442153:0.084249:0.442153:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Proposiciones de la forma si   entonces   representadas por \:@0.073090:0.496323:0.516874:0.496323:0.516874:0.480610:0.073090:0.480610:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.278202:0.496323:0.287460:0.496323:0.287460:0.479916:0.278202:0.479916:0.000000
q:@0.362672:0.496323:0.371931:0.496323:0.371931:0.479916:0.362672:0.479916:0.000000
p:@0.516668:0.496323:0.525926:0.496323:0.525926:0.479916:0.516668:0.479916:0.000000
q:@0.547712:0.496320:0.556971:0.496320:0.556971:0.479914:0.547712:0.479914:0.000000
\:@0.558370:0.496320:0.563910:0.496320:0.563910:0.480607:0.558370:0.480607:0.000000
Este tipo de proposiciones sirve para esquematizar un teorema. En este caso,   es la hipótesis y   es la tesis. :@0.073081:0.527260:0.848582:0.527260:0.848582:0.511547:0.073081:0.511547:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.631318:0.527260:0.640577:0.527260:0.640577:0.510854:0.631318:0.510854:0.000000
q:@0.761034:0.527260:0.770293:0.527260:0.770293:0.510854:0.761034:0.510854:0.000000
Ejemplo 4:@0.073081:0.558200:0.149453:0.558200:0.149453:0.541530:0.073081:0.541530:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Identifica la hipótesis y la tesis en las siguientes proposiciones::@0.073081:0.589140:0.521379:0.589140:0.521379:0.573427:0.073081:0.573427:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a.  Si Juliana tiene quince años, no puede votar en las próximas elecciones. :@0.104633:0.620067:0.656850:0.620067:0.656850:0.604355:0.104633:0.604355:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.675509:0.620067:0.679540:0.620067:0.679540:0.604355:0.675509:0.604355:0.000000
Hipótesis: Juliana tiene quince años. :@0.134754:0.636709:0.399319:0.636709:0.399319:0.620996:0.134754:0.620996:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.434541:0.636709:0.438572:0.636709:0.438572:0.620996:0.434541:0.620996:0.000000
Tesis: Juliana no puede votar en las próximas elecciones.:@0.134760:0.653351:0.540751:0.653351:0.540751:0.637638:0.134760:0.637638:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b.  Si dos rectas coplanares tienen un punto común, no son paralelas.  :@0.104633:0.684288:0.619298:0.684288:0.619298:0.668576:0.104633:0.668576:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Hipótesis: existen dos rectas coplanares que tienen un punto común. :@0.134754:0.700930:0.639305:0.700930:0.639305:0.685217:0.134754:0.685217:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.675509:0.700930:0.679540:0.700930:0.679540:0.685217:0.675509:0.685217:0.000000
Tesis: las rectas no son paralelas.:@0.134759:0.717572:0.365484:0.717572:0.365484:0.701859:0.134759:0.701859:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3.3 Reglas de inferencia:@0.085923:0.752189:0.263799:0.752189:0.263799:0.735520:0.085923:0.735520:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Modus ponendo ponens:@0.082576:0.778838:0.258917:0.778838:0.258917:0.762154:0.082576:0.762154:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 (modo que afirmando afirma) :@0.258957:0.778838:0.490976:0.778838:0.490976:0.762168:0.258957:0.762168:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.082576:0.795480:0.091835:0.795480:0.091835:0.779074:0.082576:0.779074:0.000000
q:@0.113595:0.795480:0.122854:0.795480:0.122854:0.779074:0.113595:0.779074:0.000000
: Se da  ; luego, se tiene que dar  , que se puede representar como:@0.124260:0.795480:0.609203:0.795480:0.609203:0.779767:0.124260:0.779767:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.174843:0.795480:0.184102:0.795480:0.184102:0.779074:0.174843:0.779074:0.000000
q:@0.360131:0.795480:0.369390:0.795480:0.369390:0.779074:0.360131:0.779074:0.000000
[(:@0.438840:0.823424:0.451008:0.823424:0.451008:0.805770:0.438840:0.805770:0.000000:0.000000
p:@0.450915:0.822842:0.460174:0.822842:0.460174:0.806436:0.450915:0.806436:0.000000
q:@0.481960:0.822843:0.491218:0.822843:0.491218:0.806437:0.481960:0.806437:0.000000
)⋀ ]:@0.492624:0.823425:0.530120:0.823425:0.530120:0.805771:0.492624:0.805771:0.000000:0.000000:0.000000:0.000000
p:@0.513903:0.822843:0.524064:0.822843:0.524064:0.807130:0.513903:0.807130:0.000000
q:@0.550374:0.822843:0.559633:0.822843:0.559633:0.806437:0.550374:0.806437:0.000000
p:@0.374562:0.850206:0.383821:0.850206:0.383821:0.833800:0.374562:0.833800:0.000000
q:@0.405581:0.850206:0.414840:0.850206:0.414840:0.833800:0.405581:0.833800:0.000000
 No se da  , luego no se da :@0.416246:0.850206:0.614860:0.850206:0.614860:0.834493:0.416246:0.834493:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.487261:0.850206:0.496520:0.850206:0.496520:0.833800:0.487261:0.833800:0.000000
q:@0.614676:0.850206:0.623935:0.850206:0.623935:0.833800:0.614676:0.833800:0.000000
Modus tollendo tollens :@0.082577:0.877568:0.251186:0.877568:0.251186:0.860885:0.082577:0.860885:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(modo que negando niega) :@0.251246:0.877569:0.463429:0.877569:0.463429:0.860900:0.251246:0.860900:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Se da por verdadero :@0.082576:0.894210:0.233265:0.894210:0.233265:0.878497:0.082576:0.878497:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p v q:@0.233073:0.894210:0.265654:0.894210:0.265654:0.877804:0.233073:0.877804:0.000000:0.000000:0.000000:0.000000:0.000000
. Si ~ , entonces se valida :@0.265618:0.894210:0.453419:0.894210:0.453419:0.878497:0.265618:0.878497:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
q:@0.299763:0.894210:0.309022:0.894210:0.309022:0.877804:0.299763:0.877804:0.000000
p:@0.453206:0.894210:0.462465:0.894210:0.462465:0.877804:0.453206:0.877804:0.000000
Contraposición::@0.364612:0.921572:0.484045:0.921572:0.484045:0.904902:0.364612:0.904902:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.483909:0.921572:0.487940:0.921572:0.487940:0.905859:0.483909:0.905859:0.000000
[(:@0.487867:0.922154:0.500034:0.922154:0.500034:0.904500:0.487867:0.904500:0.000000:0.000000
p:@0.499942:0.921572:0.509201:0.921572:0.509201:0.905166:0.499942:0.905166:0.000000
q:@0.530965:0.921574:0.540224:0.921574:0.540224:0.905168:0.530965:0.905168:0.000000
)⋀∙ ]:@0.541629:0.922156:0.593464:0.922156:0.593464:0.904502:0.541629:0.904502:0.000000:0.000000:0.000000:0.000000:0.000000
q:@0.578149:0.921574:0.587408:0.921574:0.587408:0.905168:0.578149:0.905168:0.000000
~:@0.613734:0.921574:0.624705:0.921574:0.624705:0.905861:0.613734:0.905861:0.000000
p:@0.624624:0.921574:0.633883:0.921574:0.633883:0.905168:0.624624:0.905168:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000