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Demonstration with completes sets

  1. Aug 21, 2011 #1
    1. We have [itex]A\subseteq \mathcal{U}[/itex]. For [itex]i_1, i_2 \in \{0,1\}[/itex]and [itex]A^0 := A^c, A^1 := A[/itex].
    A is a complete set if [itex]A\cap A_1 ^{i1} \cap A_2^{i2} \neq \emptyset[/itex] then [itex]A_1 ^{i1} \cap A_2^{i2} \subseteq A[/itex]

    Demonstrate that [itex]A_1, A_2[/itex] are complete sets too. And if A is a complete set then [itex]A^c[/itex] is a complete set too.



    2. The first part I can't get it and don't know where to begin. The second part I tried to do:
    [itex]A \cap \bigcap X \neq \emptyset \rightarrow A^c \cap (\bigcap X)^c \neq \emptyset[/itex] with [itex]\bigcap X = A_1^{i1} \cap A_2^{i2}[/itex] then [itex]A^c \subseteq (\bigcap X)^c \rightarrow A^c \subseteq (A_1^{i1})^c \cup (A_2^{i2})^c[/itex]. But when I get there I'm not sure where to go next.

    Any help would be very apreciated! Thanks
     
  2. jcsd
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