Finding B and C to Satisfy Conditions

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Homework Statement


Find B and C such that
\emptyset \in C
B \in C
B \subset C

The Attempt at a Solution


B=\emptyset
C=\{B\}
It just does not look right. Any feedback?
 
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Looks good. B is clearly an element of C, and since ##B=\varnothing##, this means that ##\varnothing## is an element of C. The subsets of C are ##\varnothing## and ##C##. Since ##B=\varnothing##, this means that B is a subset of C.
 
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There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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