Let

Let A be the finite union of elements from

Prove that A is an algebra.

Proof so far.

Let , then

I need to show that:

1.

2.

Claim 2 I think should be pretty straight forward, since the union of unions of those sets should still be in the same form.

Claim 1 I'm in trouble, I have the following:

Now, will this be equal to ? In which case I can conclude it is indeed in A?

Thank you.