Half ring $Q$ and created ring $F$ Prove

Question

$Q$ half ring on $X$ and $F=\{\bigcup\limits_{i=1}^k P_i|P_i\in Q\} $. Then F is a ring generated by Q.

I need to prove:

1. $\varnothing\in F$
2. $A\in F, B\in F \Rightarrow A\setminus B\in F$.
3. $A\in F, B\in F \Rightarrow A\cup B \in F$

I already proved 1) and 2).

For 3) I searched for a hint and did find that: $F$ is $\cap$-stable $\Rightarrow A\cup B \in F$.

I can see and prove why $F$ is $\cap$-stable but I cant understand why it must be $\cup$-stable then. Probably I miss a connection between union and intersection.

I do think I mean $\pi$-system by $\cap$-stable but I am not sure. I just translated to english.