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How many triple $(A,B,C)$ of subsets of $\{1,2,3,4\}$ satisfy to the following condition? $$(A\cap B)\subseteq C \subseteq (A\cup B)$$ I think every element of $\{1,2,3,4\}$ has 4 choice ,or in $A$ or in $B$ or in $C$ or in $\{1,2,3,4\}$ such that satisfy in condition,but it isn't all of choice because $A$ and $B$ can join .

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Let's see the following image:

enter image description here

Now in order to find any sets $A,B,C$ you just need to distribute $A=\{1,2,3,4\}$ elements in the six regions! which means that you have to correspond to every element a region in which it belong this makes $6^4$ ways

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  • $\begingroup$ how did you draw image? $\endgroup$
    – user 1
    Apr 29, 2015 at 15:43

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