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Set Theoryhard
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Let χA(x)\chi_A(x)χA​(x) denote the characteristic function of set AAA, defined as χA(x)=1\chi_A(x) = 1χA​(x)=1 if x∈Ax \in Ax∈A and χA(x)=0\chi_A(x) = 0χA​(x)=0 if x∉Ax \notin Ax∈/A. For any elements xxx in the universal set UUU, which of the following statements is equivalent to the assertion that A⊆BA \subseteq BA⊆B?