# Prove if two sets are denumerable then their union is denumerable

• October 2nd 2010, 11:04 AM
dynas7y
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.
• October 2nd 2010, 11:21 AM
Plato
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 $(S\cup T)=S\cup (S\setminus T).$