146:@0.067867:0.963104:0.109245:0.963104:0.109245:0.941283:0.067867:0.941283:0.000000:0.000000:0.000000
Matemática:@0.120102:0.956142:0.204868:0.956142:0.204868:0.943479:0.120102:0.943479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
10.º EGB:@0.120102:0.967458:0.179272:0.967458:0.179272:0.954794:0.120102:0.954794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DUA:@0.070720:0.123711:0.114363:0.123711:0.114363:0.103460:0.070720:0.103460:0.000000:0.000000:0.000000
. Representación:@0.114363:0.123082:0.246653:0.123082:0.246653:0.106182:0.114363:0.106182:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En la lógica proposicional, la equivalencia lógica se refiere a la igualdad entre :@0.292005:0.150231:0.912263:0.150231:0.912263:0.133842:0.292005:0.133842:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
proposiciones. Se utiliza el signo  , que se lee lógicamente equivalente. :@0.292005:0.166827:0.818051:0.166827:0.818051:0.150439:0.292005:0.150439:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
≡:@0.532242:0.166413:0.542359:0.166413:0.542359:0.149470:0.532242:0.149470:0.000000
Dos proposiciones son lógicamente equivalentes cuando tienen el mismo valor de :@0.292005:0.190546:0.912147:0.190546:0.912147:0.174158:0.292005:0.174158:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
verdad en todas las combinaciones; es decir, sus columnas resultado son idénticas.:@0.292005:0.207143:0.895928:0.207143:0.895928:0.190754:0.292005:0.190754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Mediante el reemplazo de una proposición por otra equivalente más simple, se :@0.292005:0.230862:0.912222:0.230862:0.912222:0.214473:0.292005:0.214473:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
pueden simplificar razonamientos y demostraciones, lo que facilita el análisis lógico :@0.292005:0.247458:0.912193:0.247458:0.912193:0.231069:0.292005:0.231069:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y la resolución de problemas.:@0.292005:0.264055:0.505338:0.264055:0.505338:0.247666:0.292005:0.247666:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Las proposiciones  ,   son equivalentes cuando sus columnas resultado son :@0.301504:0.302924:0.902704:0.302924:0.902704:0.286535:0.301504:0.286535:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p q:@0.444834:0.302924:0.474760:0.302924:0.474760:0.287531:0.444834:0.287531:0.000000:0.000000:0.000000
idénticas. Se escribe  :@0.301504:0.319520:0.456478:0.319520:0.456478:0.303131:0.301504:0.303131:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p  q p :@0.456478:0.319520:0.522949:0.319520:0.522949:0.304127:0.456478:0.304127:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
≡:@0.469064:0.319106:0.479181:0.319106:0.479181:0.302163:0.469064:0.302163:0.000000
 o :@0.492488:0.319520:0.510363:0.319520:0.510363:0.303131:0.492488:0.303131:0.000000:0.000000:0.000000
⇔:@0.522949:0.319106:0.542150:0.319106:0.542150:0.302163:0.522949:0.302163:0.000000
q:@0.546186:0.319520:0.555455:0.319520:0.555455:0.304127:0.546186:0.304127:0.000000
Ejemplos:@0.292014:0.361841:0.358482:0.361841:0.358482:0.345203:0.292014:0.345203:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Verifica si las siguientes proposiciones son equivalentes.:@0.292014:0.385560:0.699607:0.385560:0.699607:0.369171:0.292014:0.369171:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a) :@0.292014:0.409279:0.310036:0.409279:0.310036:0.392655:0.292014:0.392655:0.000000:0.000000:0.000000
p:@0.315748:0.409279:0.325017:0.409279:0.325017:0.393886:0.315748:0.393886:0.000000
→:@0.329053:0.408864:0.347241:0.408864:0.347241:0.391922:0.329053:0.391922:0.000000
q:@0.351277:0.409279:0.360546:0.409279:0.360546:0.393886:0.351277:0.393886:0.000000
  y :@0.360546:0.409279:0.380761:0.409279:0.380761:0.392890:0.360546:0.392890:0.000000:0.000000:0.000000:0.000000
∼  ∨:@0.380761:0.408864:0.419901:0.408864:0.419901:0.391922:0.380761:0.391922:0.000000:0.000000:0.000000:0.000000
p:@0.395485:0.409279:0.404754:0.409279:0.404754:0.393886:0.395485:0.393886:0.000000
q:@0.423937:0.409279:0.433206:0.409279:0.433206:0.393886:0.423937:0.393886:0.000000
b):@0.578471:0.409279:0.594687:0.409279:0.594687:0.392378:0.578471:0.392378:0.000000:0.000000
p:@0.605283:0.409279:0.614552:0.409279:0.614552:0.393886:0.605283:0.393886:0.000000
∧  →:@0.618588:0.408864:0.670683:0.408864:0.670683:0.391922:0.618588:0.391922:0.000000:0.000000:0.000000:0.000000
(:@0.634307:0.409279:0.639190:0.409279:0.639190:0.392890:0.634307:0.392890:0.000000
q:@0.639190:0.409279:0.648459:0.409279:0.648459:0.393886:0.639190:0.393886:0.000000
r:@0.674719:0.409279:0.680007:0.409279:0.680007:0.393886:0.674719:0.393886:0.000000
) y (:@0.680007:0.409279:0.705954:0.409279:0.705954:0.392890:0.680007:0.392890:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.705954:0.409279:0.715223:0.409279:0.715223:0.393886:0.705954:0.393886:0.000000
∧:@0.719258:0.408864:0.730370:0.408864:0.730370:0.391922:0.719258:0.391922:0.000000
q:@0.734406:0.409279:0.743675:0.409279:0.743675:0.393886:0.734406:0.393886:0.000000
)   (:@0.743675:0.409279:0.779701:0.409279:0.779701:0.392890:0.743675:0.392890:0.000000:0.000000:0.000000:0.000000:0.000000
→:@0.752594:0.408864:0.770782:0.408864:0.770782:0.391922:0.752594:0.391922:0.000000
p:@0.779701:0.409279:0.788970:0.409279:0.788970:0.393886:0.779701:0.393886:0.000000
∧ :@0.793006:0.408864:0.808724:0.408864:0.808724:0.391922:0.793006:0.391922:0.000000:0.000000
r:@0.808724:0.409279:0.814013:0.409279:0.814013:0.393886:0.808724:0.393886:0.000000
):@0.814013:0.409279:0.818897:0.409279:0.818897:0.392890:0.814013:0.392890:0.000000
Solución:@0.292014:0.440135:0.355792:0.440135:0.355792:0.423497:0.292014:0.423497:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Elaboramos las tablas de verdad para cada proposición compuesta.:@0.292014:0.463854:0.784044:0.463854:0.784044:0.447465:0.292014:0.447465:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a) :@0.292014:0.487573:0.310036:0.487573:0.310036:0.470948:0.292014:0.470948:0.000000:0.000000:0.000000
p:@0.315748:0.487573:0.325017:0.487573:0.325017:0.472179:0.315748:0.472179:0.000000
→:@0.329053:0.487158:0.347241:0.487158:0.347241:0.470215:0.329053:0.470215:0.000000
q:@0.351277:0.487573:0.360546:0.487573:0.360546:0.472179:0.351277:0.472179:0.000000
  y :@0.360546:0.487573:0.380761:0.487573:0.380761:0.471184:0.360546:0.471184:0.000000:0.000000:0.000000:0.000000
∼  ∨:@0.380761:0.487158:0.419901:0.487158:0.419901:0.470215:0.380761:0.470215:0.000000:0.000000:0.000000:0.000000
p:@0.395485:0.487573:0.404754:0.487573:0.404754:0.472179:0.395485:0.472179:0.000000
q:@0.423937:0.487573:0.433206:0.487573:0.433206:0.472179:0.423937:0.472179:0.000000
p:@0.460033:0.516175:0.469448:0.516175:0.469448:0.500622:0.460033:0.500622:0.000000
q:@0.521783:0.516175:0.531164:0.516175:0.531164:0.500622:0.521783:0.500622:0.000000
∼ :@0.576139:0.516234:0.590863:0.516234:0.590863:0.499292:0.576139:0.499292:0.000000:0.000000
p:@0.590860:0.516335:0.600274:0.516335:0.600274:0.500782:0.590860:0.500782:0.000000
p:@0.639291:0.517114:0.648706:0.517114:0.648706:0.501561:0.639291:0.501561:0.000000
→:@0.652736:0.517017:0.670924:0.517017:0.670924:0.500075:0.652736:0.500075:0.000000
q:@0.674957:0.517118:0.684338:0.517118:0.684338:0.501565:0.674957:0.501565:0.000000
∼  ∨:@0.710487:0.517017:0.749640:0.517017:0.749640:0.500075:0.710487:0.500075:0.000000:0.000000:0.000000:0.000000
p:@0.725207:0.517118:0.734622:0.517118:0.734622:0.501565:0.725207:0.501565:0.000000
q:@0.753547:0.517118:0.762928:0.517118:0.762928:0.501565:0.753547:0.501565:0.000000
V:@0.460481:0.538706:0.469008:0.538706:0.469008:0.523807:0.460481:0.523807:0.000000
V:@0.522213:0.538706:0.530740:0.538706:0.530740:0.523807:0.522213:0.523807:0.000000
F:@0.584348:0.538706:0.592088:0.538706:0.592088:0.523807:0.584348:0.523807:0.000000
V:@0.657556:0.538706:0.666083:0.538706:0.666083:0.523807:0.657556:0.523807:0.000000
V:@0.743027:0.538706:0.751554:0.538706:0.751554:0.523807:0.743027:0.523807:0.000000
V:@0.460481:0.558194:0.469008:0.558194:0.469008:0.543295:0.460481:0.543295:0.000000
F:@0.522615:0.558194:0.530355:0.558194:0.530355:0.543295:0.522615:0.543295:0.000000
F:@0.584348:0.558194:0.592088:0.558194:0.592088:0.543295:0.584348:0.543295:0.000000
F:@0.657958:0.558194:0.665698:0.558194:0.665698:0.543295:0.657958:0.543295:0.000000
F:@0.743429:0.558194:0.751168:0.558194:0.751168:0.543295:0.743429:0.543295:0.000000
F:@0.460883:0.577682:0.468622:0.577682:0.468622:0.562783:0.460883:0.562783:0.000000
V:@0.522230:0.577682:0.530757:0.577682:0.530757:0.562783:0.522230:0.562783:0.000000
V:@0.583963:0.577682:0.592490:0.577682:0.592490:0.562783:0.583963:0.562783:0.000000
V:@0.657573:0.577682:0.666100:0.577682:0.666100:0.562783:0.657573:0.562783:0.000000
V:@0.743043:0.577682:0.751570:0.577682:0.751570:0.562783:0.743043:0.562783:0.000000
F:@0.460883:0.597170:0.468622:0.597170:0.468622:0.582271:0.460883:0.582271:0.000000
F:@0.522615:0.597170:0.530355:0.597170:0.530355:0.582271:0.522615:0.582271:0.000000
V:@0.583963:0.597170:0.592490:0.597170:0.592490:0.582271:0.583963:0.582271:0.000000
V:@0.657573:0.597170:0.666100:0.597170:0.666100:0.582271:0.657573:0.582271:0.000000
V:@0.743043:0.597170:0.751570:0.597170:0.751570:0.582271:0.743043:0.582271:0.000000
 :@0.292005:0.621397:0.296041:0.621397:0.296041:0.605008:0.292005:0.605008:0.000000
  Las columnas resultado son idénticas, luego las proposiciones son equivalentes, :@0.315749:0.621397:0.912196:0.621397:0.912196:0.605008:0.315749:0.605008:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es decir: :@0.315740:0.637993:0.379627:0.637993:0.379627:0.621605:0.315740:0.621605:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.379627:0.637993:0.388896:0.637993:0.388896:0.622600:0.379627:0.622600:0.000000
→:@0.392933:0.637579:0.411121:0.637579:0.411121:0.620636:0.392933:0.620636:0.000000
q:@0.415157:0.637993:0.424426:0.637993:0.424426:0.622600:0.415157:0.622600:0.000000
  :@0.424426:0.637993:0.432497:0.637993:0.432497:0.621605:0.424426:0.621605:0.000000:0.000000
≡ ∼  ∨:@0.432497:0.637579:0.485790:0.637579:0.485790:0.620636:0.432497:0.620636:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.461374:0.637993:0.470643:0.637993:0.470643:0.622600:0.461374:0.622600:0.000000
q:@0.489826:0.637993:0.499095:0.637993:0.499095:0.622600:0.489826:0.622600:0.000000
b) :@0.292005:0.661712:0.311575:0.661712:0.311575:0.645088:0.292005:0.645088:0.000000:0.000000:0.000000
p:@0.315740:0.661712:0.325009:0.661712:0.325009:0.646319:0.315740:0.646319:0.000000
∧  →:@0.329045:0.661298:0.381140:0.661298:0.381140:0.644355:0.329045:0.644355:0.000000:0.000000:0.000000:0.000000
(:@0.344763:0.661712:0.349647:0.661712:0.349647:0.645324:0.344763:0.645324:0.000000
q:@0.349647:0.661712:0.358916:0.661712:0.358916:0.646319:0.349647:0.646319:0.000000
r:@0.385175:0.661712:0.390464:0.661712:0.390464:0.646319:0.385175:0.646319:0.000000
) y (:@0.390464:0.661712:0.416410:0.661712:0.416410:0.645324:0.390464:0.645324:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.416410:0.661712:0.425679:0.661712:0.425679:0.646319:0.416410:0.646319:0.000000
∧:@0.429715:0.661298:0.440827:0.661298:0.440827:0.644355:0.429715:0.644355:0.000000
q:@0.444862:0.661712:0.454132:0.661712:0.454132:0.646319:0.444862:0.646319:0.000000
)   (:@0.454132:0.661712:0.490158:0.661712:0.490158:0.645324:0.454132:0.645324:0.000000:0.000000:0.000000:0.000000:0.000000
→:@0.463050:0.661298:0.481239:0.661298:0.481239:0.644355:0.463050:0.644355:0.000000
p:@0.490158:0.661712:0.499427:0.661712:0.499427:0.646319:0.490158:0.646319:0.000000
∧ :@0.503462:0.661298:0.519181:0.661298:0.519181:0.644355:0.503462:0.644355:0.000000:0.000000
r:@0.519181:0.661712:0.524470:0.661712:0.524470:0.646319:0.519181:0.646319:0.000000
):@0.524470:0.661712:0.529353:0.661712:0.529353:0.645324:0.524470:0.645324:0.000000
p:@0.342160:0.690306:0.351575:0.690306:0.351575:0.674753:0.342160:0.674753:0.000000
q:@0.403910:0.690306:0.413291:0.690306:0.413291:0.674753:0.403910:0.674753:0.000000
r:@0.467234:0.690306:0.473432:0.690306:0.473432:0.674753:0.467234:0.674753:0.000000
p  (q:@0.541681:0.691249:0.584458:0.691250:0.584458:0.675697:0.541681:0.675696:0.000000:0.000000:0.000000:0.000000:0.000000
∧ :@0.554182:0.691150:0.569901:0.691150:0.569901:0.674208:0.554182:0.674208:0.000000:0.000000
→:@0.588494:0.691150:0.606682:0.691150:0.606682:0.674208:0.588494:0.674208:0.000000
r):@0.610714:0.691250:0.622173:0.691250:0.622173:0.675697:0.610714:0.675697:0.000000:0.000000
(p:@0.723324:0.691250:0.737999:0.691250:0.737999:0.675697:0.723324:0.675697:0.000000:0.000000
∧  → :@0.742042:0.691150:0.798281:0.691150:0.798281:0.674208:0.742042:0.674208:0.000000:0.000000:0.000000:0.000000:0.000000
q) :@0.757762:0.691250:0.775486:0.691250:0.775486:0.675697:0.757762:0.675697:0.000000:0.000000:0.000000
(p:@0.798278:0.691250:0.812953:0.691250:0.812953:0.675697:0.798278:0.675697:0.000000:0.000000
∧ :@0.816987:0.691150:0.832706:0.691150:0.832706:0.674208:0.816987:0.674208:0.000000:0.000000
r):@0.832707:0.691250:0.844166:0.691250:0.844166:0.675697:0.832707:0.675697:0.000000:0.000000
V:@0.342599:0.713781:0.351126:0.713781:0.351126:0.698882:0.342599:0.698882:0.000000
V:@0.404332:0.713781:0.412859:0.713781:0.412859:0.698882:0.404332:0.698882:0.000000
V:@0.466064:0.713781:0.474591:0.713781:0.474591:0.698882:0.466064:0.698882:0.000000
V:@0.537295:0.713781:0.545822:0.713781:0.545822:0.698882:0.537295:0.698882:0.000000
V:@0.618025:0.713781:0.626552:0.713781:0.626552:0.698882:0.618025:0.698882:0.000000
V:@0.698755:0.713781:0.707282:0.713781:0.707282:0.698882:0.698755:0.698882:0.000000
V:@0.779485:0.713781:0.788012:0.713781:0.788012:0.698882:0.779485:0.698882:0.000000
V:@0.860215:0.713781:0.868742:0.713781:0.868742:0.698882:0.860215:0.698882:0.000000
V:@0.342599:0.735168:0.351126:0.735168:0.351126:0.720269:0.342599:0.720269:0.000000
V:@0.404332:0.735168:0.412859:0.735168:0.412859:0.720269:0.404332:0.720269:0.000000
F:@0.466466:0.735168:0.474206:0.735168:0.474206:0.720269:0.466466:0.720269:0.000000
F:@0.537698:0.735168:0.545437:0.735168:0.545437:0.720269:0.537698:0.720269:0.000000
F:@0.618427:0.735168:0.626167:0.735168:0.626167:0.720269:0.618427:0.720269:0.000000
V:@0.698755:0.735168:0.707282:0.735168:0.707282:0.720269:0.698755:0.720269:0.000000
F:@0.779870:0.735168:0.787610:0.735168:0.787610:0.720269:0.779870:0.720269:0.000000
F:@0.860600:0.735168:0.868340:0.735168:0.868340:0.720269:0.860600:0.720269:0.000000
V:@0.342599:0.756554:0.351126:0.756554:0.351126:0.741655:0.342599:0.741655:0.000000
F:@0.404734:0.756554:0.412473:0.756554:0.412473:0.741655:0.404734:0.741655:0.000000
V:@0.466081:0.756554:0.474608:0.756554:0.474608:0.741655:0.466081:0.741655:0.000000
V:@0.537312:0.756554:0.545839:0.756554:0.545839:0.741655:0.537312:0.741655:0.000000
V:@0.618042:0.756554:0.626569:0.756554:0.626569:0.741655:0.618042:0.741655:0.000000
F:@0.699157:0.756554:0.706897:0.756554:0.706897:0.741655:0.699157:0.741655:0.000000
V:@0.779485:0.756554:0.788012:0.756554:0.788012:0.741655:0.779485:0.741655:0.000000
V:@0.860215:0.756554:0.868742:0.756554:0.868742:0.741655:0.860215:0.741655:0.000000
V:@0.342599:0.777941:0.351126:0.777941:0.351126:0.763042:0.342599:0.763042:0.000000
F:@0.404734:0.777941:0.412473:0.777941:0.412473:0.763042:0.404734:0.763042:0.000000
F:@0.466466:0.777941:0.474206:0.777941:0.474206:0.763042:0.466466:0.763042:0.000000
V:@0.537295:0.777941:0.545822:0.777941:0.545822:0.763042:0.537295:0.763042:0.000000
V:@0.618025:0.777941:0.626552:0.777941:0.626552:0.763042:0.618025:0.763042:0.000000
F:@0.699140:0.777941:0.706880:0.777941:0.706880:0.763042:0.699140:0.763042:0.000000
V:@0.779468:0.777941:0.787995:0.777941:0.787995:0.763042:0.779468:0.763042:0.000000
F:@0.860583:0.777941:0.868323:0.777941:0.868323:0.763042:0.860583:0.763042:0.000000
F:@0.342968:0.799328:0.350707:0.799328:0.350707:0.784429:0.342968:0.784429:0.000000
V:@0.404315:0.799328:0.412842:0.799328:0.412842:0.784429:0.404315:0.784429:0.000000
V:@0.466047:0.799328:0.474574:0.799328:0.474574:0.784429:0.466047:0.784429:0.000000
F:@0.537664:0.799328:0.545404:0.799328:0.545404:0.784429:0.537664:0.784429:0.000000
V:@0.617992:0.799328:0.626519:0.799328:0.626519:0.784429:0.617992:0.784429:0.000000
F:@0.699107:0.799328:0.706846:0.799328:0.706846:0.784429:0.699107:0.784429:0.000000
V:@0.779435:0.799328:0.787962:0.799328:0.787962:0.784429:0.779435:0.784429:0.000000
F:@0.860550:0.799328:0.868289:0.799328:0.868289:0.784429:0.860550:0.784429:0.000000
F:@0.342934:0.820715:0.350674:0.820715:0.350674:0.805816:0.342934:0.805816:0.000000
V:@0.404281:0.820715:0.412808:0.820715:0.412808:0.805816:0.404281:0.805816:0.000000
F:@0.466416:0.820715:0.474156:0.820715:0.474156:0.805816:0.466416:0.805816:0.000000
F:@0.537647:0.820715:0.545387:0.820715:0.545387:0.805816:0.537647:0.805816:0.000000
F:@0.618377:0.820715:0.626117:0.820715:0.626117:0.805816:0.618377:0.805816:0.000000
F:@0.699107:0.820715:0.706846:0.820715:0.706846:0.805816:0.699107:0.805816:0.000000
V:@0.779435:0.820715:0.787962:0.820715:0.787962:0.805816:0.779435:0.805816:0.000000
F:@0.860550:0.820715:0.868289:0.820715:0.868289:0.805816:0.860550:0.805816:0.000000
F:@0.342934:0.842101:0.350674:0.842101:0.350674:0.827202:0.342934:0.827202:0.000000
F:@0.404667:0.842101:0.412406:0.842101:0.412406:0.827202:0.404667:0.827202:0.000000
V:@0.466014:0.842101:0.474541:0.842101:0.474541:0.827202:0.466014:0.827202:0.000000
F:@0.537630:0.842101:0.545370:0.842101:0.545370:0.827202:0.537630:0.827202:0.000000
V:@0.617958:0.842101:0.626485:0.842101:0.626485:0.827202:0.617958:0.827202:0.000000
F:@0.699073:0.842101:0.706813:0.842101:0.706813:0.827202:0.699073:0.827202:0.000000
V:@0.779401:0.842101:0.787928:0.842101:0.787928:0.827202:0.779401:0.827202:0.000000
F:@0.860516:0.842101:0.868256:0.842101:0.868256:0.827202:0.860516:0.827202:0.000000
F:@0.342901:0.863488:0.350640:0.863488:0.350640:0.848589:0.342901:0.848589:0.000000
F:@0.404633:0.863488:0.412373:0.863488:0.412373:0.848589:0.404633:0.848589:0.000000
F:@0.466366:0.863488:0.474105:0.863488:0.474105:0.848589:0.466366:0.848589:0.000000
F:@0.537597:0.863488:0.545337:0.863488:0.545337:0.848589:0.537597:0.848589:0.000000
V:@0.617925:0.863488:0.626452:0.863488:0.626452:0.848589:0.617925:0.848589:0.000000
F:@0.699040:0.863488:0.706779:0.863488:0.706779:0.848589:0.699040:0.848589:0.000000
V:@0.779368:0.863488:0.787895:0.863488:0.787895:0.848589:0.779368:0.848589:0.000000
F:@0.860483:0.863488:0.868222:0.863488:0.868222:0.848589:0.860483:0.848589:0.000000
 :@0.292005:0.888648:0.296041:0.888648:0.296041:0.872259:0.292005:0.872259:0.000000
  Las  columnas  resultado  no  son  iguales;  por  tanto,  las  proposiciones  no  son :@0.315749:0.888648:0.912187:0.888648:0.912187:0.872259:0.315749:0.872259:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
equivalentes.:@0.315740:0.905244:0.412115:0.905244:0.412115:0.888855:0.315740:0.888855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Equivalencias lógicas. :@0.286308:0.063945:0.671720:0.063945:0.671720:0.027071:0.286308:0.027071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Tautología y contradicción:@0.286308:0.094120:0.749317:0.094120:0.749317:0.057246:0.286308:0.057246:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.094760:0.108604:0.183816:0.108604:0.183816:0.011516:0.094760:0.011516:0.000000:0.000000
Los algoritmos de :@0.126803:0.204499:0.249228:0.204499:0.249228:0.189600:0.126803:0.189600:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
inteligencia artificial se :@0.094638:0.219586:0.249228:0.219586:0.249228:0.204687:0.094638:0.204687:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
basan en la lógica :@0.126585:0.234674:0.249228:0.234674:0.249228:0.219775:0.126585:0.219775:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática.:@0.163039:0.249762:0.245561:0.249762:0.245561:0.234863:0.163039:0.234863:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Digital:@0.147511:0.171774:0.197981:0.171774:0.197981:0.154873:0.147511:0.154873:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si hay dificultades :@0.126401:0.481619:0.249230:0.481619:0.249230:0.466720:0.126401:0.466720:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
visuales, es necesario :@0.105343:0.496707:0.249226:0.496707:0.249226:0.481808:0.105343:0.481808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ayudarnos unos a otros, :@0.087485:0.511794:0.249228:0.511794:0.249228:0.496895:0.087485:0.496895:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ya sea con una :@0.146755:0.526882:0.249230:0.526882:0.249230:0.511983:0.146755:0.511983:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
explicación de los sucesos :@0.070900:0.541970:0.249230:0.541970:0.249230:0.527071:0.070900:0.527071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
visuales o con un :@0.130656:0.557057:0.249230:0.557057:0.249230:0.542158:0.130656:0.542158:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
resumen de lo que :@0.119901:0.572145:0.249230:0.572145:0.249230:0.557246:0.119901:0.557246:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sucede alrededor.:@0.127507:0.587232:0.245559:0.587232:0.245559:0.572333:0.127507:0.572333:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  Ética e integridad:@0.112631:0.448895:0.251858:0.448895:0.251858:0.431995:0.112631:0.431995:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Procura fomentar la :@0.114825:0.722850:0.249230:0.722850:0.249230:0.707951:0.114825:0.707951:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
auto­reflexión sobre tus :@0.087368:0.737938:0.249228:0.737938:0.249228:0.723039:0.087368:0.723039:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
emociones y reacciones :@0.085659:0.753025:0.249228:0.753025:0.249228:0.738126:0.085659:0.738126:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en diferentes situaciones. :@0.077534:0.768113:0.249226:0.768113:0.249226:0.753214:0.077534:0.753214:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Lleva un diario emocional :@0.073782:0.783200:0.249228:0.783200:0.249228:0.768301:0.073782:0.768301:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
o participa en discusiones :@0.072559:0.798288:0.249228:0.798288:0.249228:0.783389:0.072559:0.783389:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
grupales donde se :@0.122012:0.813376:0.249230:0.813376:0.249230:0.798477:0.122012:0.798477:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
analicen experiencias :@0.102897:0.828463:0.249228:0.828463:0.249228:0.813564:0.102897:0.813564:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
emocionales para la toma :@0.073530:0.843551:0.249228:0.843551:0.249228:0.828652:0.073530:0.828652:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de decisiones.:@0.151697:0.858639:0.245559:0.858639:0.245559:0.843739:0.151697:0.843739:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
        Socioemocional:@0.095552:0.690408:0.245195:0.690408:0.245195:0.673507:0.095552:0.673507:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.4.2.2. :@0.290067:0.965521:0.332119:0.965521:0.332119:0.954766:0.290067:0.954766:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definir y reconocer una tautología para la construcción de tablas de verdad.:@0.332119:0.965521:0.684946:0.965521:0.684946:0.955091:0.332119:0.955091:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.348302:0.965521:0.350870:0.965521:0.350870:0.955091:0.348302:0.955091:0.000000
M.4.1.63.:@0.272234:0.740428:0.272234:0.710276:0.258338:0.710276:0.258338:0.740428:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000