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 cs-401r:set-theory-identities [2014/09/09 14:52]ringger cs-401r:set-theory-identities [2014/10/06 07:08]ringger [Further Reference] Both sides previous revision Previous revision 2014/10/06 07:08 ringger [Further Reference] 2014/09/09 21:00 ringger [Other Useful Identities] 2014/09/09 20:57 ringger 2014/09/09 14:52 ringger 2014/09/09 14:44 ringger 2014/09/09 14:44 ringger 2014/09/05 08:09 ringger 2014/09/05 08:09 ringger created Next revision Previous revision 2014/10/06 07:08 ringger [Further Reference] 2014/09/09 21:00 ringger [Other Useful Identities] 2014/09/09 20:57 ringger 2014/09/09 14:52 ringger 2014/09/09 14:44 ringger 2014/09/09 14:44 ringger 2014/09/05 08:09 ringger 2014/09/05 08:09 ringger created Line 1: Line 1: + = Set Theory Identities = \begin{align} \begin{align} A \cup  \overline{A} & = & \Omega ​ \qquad & \mbox{Complementation law}\\ A \cup  \overline{A} & = & \Omega ​ \qquad & \mbox{Complementation law}\\ Line 24: Line 25: \begin{align} \begin{align} B - A \equiv B \cap \overline{A} \qquad & \mbox{Definition of set difference} \\ B - A \equiv B \cap \overline{A} \qquad & \mbox{Definition of set difference} \\ - \left(R \cap S\right) \cup \left(R \cap \overline{S}\right) ​\equiv ​R + \left(R \cap S\right) \cup \left(R \cap \overline{S}\right) ​= R \end{align} \end{align} == Further Reference == == Further Reference == + + You may use the identities available in the following Wikipedia article, as long as they are not the identity you are currently trying to prove: [http://​en.wikipedia.org/​wiki/​Algebra_of_sets Article on the "​algebra of sets" on Wikipedia.] [http://​en.wikipedia.org/​wiki/​Algebra_of_sets Article on the "​algebra of sets" on Wikipedia.] +