Leyes del Álgebra de Conjuntos

• 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
• $$\mbox{A} \cup \mbox{U} = \mbox{U}$$
• $$\mbox{A} \cup \varnothing = \mbox{A}$$
• $$\mbox{A} \cap \mbox{U} = \mbox{A}$$
• $$\mbox{A} \cap \varnothing = \varnothing$$

Links:

https://es.wikipedia.org/wiki/%C3%81lgebra_de_conjuntos
https://es.wikipedia.org/wiki/Diferencia_sim%C3%A9trica

https://sites.google.com/site/algebrasistemas/leyes-del-lgebra-de-conjuntos

http://es.slideshare.net/pgandarilla/leyes-de-conjuntos