Algebra of sets

An Algebra of sets is sometimes called a Boolean algebra

We will show later that every Algebra of sets is an Algebra of sets

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TODO: what could this mean?

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Definition

An class [ilmath]R[/ilmath] of sets is an Algebra of sets if:

• [math][A\in R\wedge B\in R]\implies A\cup B\in R[/math]
• [math]A\in R\implies A^c\in R[/math]

So an Algebra of sets is just a Ring of sets containing the entire set it is a set of subsets of!

Every Algebra is also a Ring

Since for [math]A\in R[/math] and [math]B\in R[/math] we have:

[math]A-B=A\cap B' = (A'\cup B)'[/math] we see that being closed under Complement and Union means it is closed under Set subtraction

Thus it is a Ring of sets

See also

• [ilmath]\sigma[/ilmath]-algebra
• Ring of sets
• Types of set algebras