Help plz ! we say that 1) x\inuuu_(n\inN)A_n if x\inA_n for some n\inN and 2)x\innnn_(n\inN)A_n if x\inA_n for all n\inN prove or dispprove nnn_(n\inN)A_n\sube uuu_(n\inN)A_n for any index set N ?
1 Answer
True.
Explanation:
Let's call the intersection of all sets
We want to prove that
So, we need to show that
We only need to recall the definition, and everything gets really simple: if we assume that
So, if we assume that
On the other hand, if we know that
This is enough to prove that the set given by the intersection is a subset of the set given by the union.