- Idempotencia
- $$\mbox{A} \cup \mbox{A} = \mbox{A}$$
- $$\mbox{A} \cap \mbox{A} = \mbox{A}$$
- Absorción
- $$\mbox{A} \cup (\mbox{A} \cap \mbox{B}) = \mbox{A}$$
- $$\mbox{A} \cap (\mbox{A} \cup \mbox{B}) = \mbox{A}$$
- $$\mbox{A} \cup (\mbox{A}^c \cap \mbox{B}) = \mbox{A} \cup \mbox{B}$$
- $$\mbox{A} \cap (\mbox{A}^c \cup \mbox{B}) = \mbox{A} \cap \mbox{B}$$
- Conmutativa
- $$\mbox{A} \cup \mbox{B}= \mbox{B} \cup \mbox{A}$$
- $$\mbox{A} \cap \mbox{B}= \mbox{B} \cup \mbox{A}$$
- Asociativa
- $$ (\mbox{A} \cup \mbox{B}) \cup \mbox{C} =\mbox{A} \cup (\mbox{B} \cup \mbox{C})$$
- $$ (\mbox{A} \cap \mbox{B}) \cap \mbox{C} =\mbox{A} \cap (\mbox{B} \cap \mbox{C})$$
- Distributiva
- $$ \mbox{A} \cup (\mbox{B} \cap \mbox{C}) =(\mbox{A} \cup \mbox{B}) \cap (\mbox{A} \cup \mbox{C})$$
- $$ \mbox{A} \cap (\mbox{B} \cup \mbox{C}) =(\mbox{A} \cap \mbox{B}) \cup (\mbox{A} \cap \mbox{C})$$
- Morgan
- $$(\mbox{A} \cup \mbox{B})^c = \mbox{A}^c \cap \mbox{B}^c$$
- $$(\mbox{A} \cap \mbox{B})^c = \mbox{A}^c \cup \mbox{B}^c$$
- Diferencia
- $$\mbox{A} - \mbox{B} = \mbox{A} \cap \mbox{B}^c$$
- Diferencia Simética
- $$\mbox{A} \Delta \mbox{B} = (\mbox{A} - \mbox{B}) \cup (\mbox{B} - \mbox{A})$$
- $$\mbox{A} \Delta \mbox{B} = (\mbox{A} \cup \mbox{B}) - (\mbox{B} \cup \mbox{A})$$
- Complemento
- $$ (\mbox{A}^c)^c = \mbox{A} $$
- $$ \mbox{A} \cup \mbox{A}^c = \mbox{U}$$
- $$ \mbox{A} \cap \mbox{A}^c = \varnothing$$
- $$ \mbox{U}^c = \varnothing $$
- $$ \varnothing^c = \mbox{U} $$
- Identidad
- $$ \mbox{A} \cup \mbox{U} = \mbox{U} $$
- $$ \mbox{A} \cup \varnothing = \mbox{A} $$
- $$ \mbox{A} \cap \mbox{U} = \mbox{A} $$
- $$ \mbox{A} \cap \varnothing = \varnothing $$
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