Studying for an exam and just want to check this "degenerate" case.
I know in boolean algebra, A + A = A. So I assume that same would hold true in set notation. My proof is as follows:
$P(A \cup A) = P(A) + P(A) - P(A \cap A) = P(A)$
I couldn't find this anywhere else but just wanted to double check here.
As a sidenote, I guess this means that $P(A \cap A) = P(A \cup A) = P(A)$?
Thanks so much.