see this screen shot and answer this question thanks!

6. (for graduate credit) A aalgebra, d, is said to be countably generated if there exists a countable collection of sets, 52%, such that 0(%) = .521. Let .971, 92, . . . be a sequence of countablygenerated (Jralgebras, and let 37 = 0(U:=1 3?\"). Show that .9? is countably generated. HINT: For each n, let 9,? be a countable collection of sets that generates 9'\". Then 0(U:=1 9}?) is countably generated (why?) Show that 0(U:=1 9,2) = 9' by using minimality arguments to show subset in both directions