Nature of D-finite sets. A is called D-finite if A is not containing countable subset. 
With the above strange definition I need to show the following two properties:


*

*For a D-finite set A, and finite B, the union of A and B is D-finite.

*The union of two D-finite sets is D-finite.
By the way, can we construct such D-finite set? 
Only hints...
Thank you.

Hints only:
The first property may be shown directly.
The second however... Try showing what happens when the union of two sets is not D-finite.
Hope it helps.
