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Rereading the notes of a proof based course I took last year I encountered the following exercise:

Let $\phi\neq C\subset P(E)$. $C$ is called and algebra if it satisfies: $$\forall A,B\in C ~[A\cup B\in C~ \wedge~A\cap B\in C ~\wedge E\setminus A\in C]$$

1-) Show that $\phi\in C$ and that $E\in C$.

2-) Show that the intersection of algebras is an algebra.

I have two questions regarding the exercise: 1. Is the definition of an algebra provided in the exercise an actual definition? Or is it just a definition my professor came up with? 2. What area of mathematics is the exercise related to?

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See the Wikipedia page on field of sets.

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