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11. De acuerdo con las leyes del álgebra de eventos, ¿cuál de las siguientes opciones es equivalente a la expresión [tex]\( A^C \cap B^C \)[/tex]?

A) [tex]\( (A \cup B)^C \)[/tex]

B) [tex]\( A \cap B \)[/tex]

C) [tex]\( (A \cap B)^C \)[/tex]

Sagot :

GinnyAnswer
Para resolver la expresión [tex]\( A^C \cap B^C \)[/tex] usando las leyes del álgebra de eventos, podemos utilizar las leyes de De Morgan. Las leyes de De Morgan nos dicen lo siguiente:

1. [tex]\((A \cap B)^C = A^C \cup B^C\)[/tex]
2. [tex]\((A \cup B)^C = A^C \cap B^C\)[/tex]

En este caso, queremos simplificar la expresión [tex]\( A^C \cap B^C \)[/tex].

Usando las leyes de De Morgan, sabemos que:
[tex]\[ (A \cup B)^C = A^C \cap B^C \][/tex]

Esto significa que [tex]\( A^C \cap B^C \)[/tex] es equivalente a [tex]\( (A \cup B)^C \)[/tex].

Por lo tanto, la opción correcta es la:

A) [tex]\((A \cup B)^C\)[/tex]
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