Math Help - Prove if two sets are denumerable then their union is denumerable

1. Prove if two sets are denumerable then their union is denumerable

Prove in detail that if S and T are denumerable, then (S U T) is denumerable. Thanks for any help.

2. Can you prove that the union of two disjoint countable set is countable?
Can you prove that any subset of a countable set is countable?

Then consider $(S\cup T)=S\cup (S\setminus T).$