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.