My instructor on measure theory solved this problem in class but I am having serious problem in understanding it's proof although I am clear with definitions.
Problem is - Let $P$ be a set and any set $A$ belongs to $P$ iff either cardinality of $A$ is finite or cardinality of Compliment of A is finite. ( it is easy to see $A$ is an algebra) . Define $Q$ to be a set such that any set $B$ belongs to $Q$ iff either Cardinality of $B$ is countable or cardinality of complement of $B$ is countable . ( I proved it to be $ \sigma $ algebra. ) Define $ \sigma ( P)$ = smallest $ \sigma $ algebra containing P.
I have to prove that $ \sigma (P) = Q $.
Can somebody give explanation on how to prove it ?