# Definition:The Algebra of Sets

## Definition

Let $E$ be a universal set.

The power set $\powerset E$, together with:

the binary operations union $\cup$ and intersection $\cap$
the unary operation complement $\complement$

is referred to as the algebra of sets on $E$.

## Also defined as

Note that the concept of an algebra of sets is a more specific concept that is applied to a subset of $\powerset E$ that is closed under union, intersection and complement, and also has a unit.

So while the algebra of sets is an algebra of sets, the reverse is not necessarily true.

## Historical Note

The concept of an algebra of sets was invented by George Boole, after whom Boolean algebra was named.