# Question regarding the given definition of algebra

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?

## 1 Answer

See the Wikipedia page on field of sets.