# 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 **for all** **at least one**

So, if we assume that **all** the sets **at least one** of the

On the other hand, if we know that **at least one** of the **all** the

This is enough to prove that the set given by the intersection is a subset of the set given by the union.