Finding B and C to Satisfy Conditions

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SUMMARY

The discussion focuses on finding sets B and C that satisfy specific conditions: the empty set must be an element of C, B must be an element of C, and B must be a subset of C. The proposed solution is B = ∅ and C = {B}, which meets all conditions. The feedback confirms that B is indeed an element of C, and since B is the empty set, it follows that ∅ is also an element of C. Therefore, the solution is valid and correctly demonstrates the relationships between the sets.

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Homework Statement


Find B and C such that
[tex]\emptyset \in C[/tex]
[tex]B \in C[/tex]
[tex]B \subset C[/tex]

The Attempt at a Solution


[tex]B=\emptyset[/tex]
[tex]C=\{B\}[/tex]
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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