Construct a subset of XY plane R^2 that is:

a) closed under vector addition & subtraction, but not under scalar multiplication

b) closed under scalar multiplication, but not vector addition & subtraction

Based on your question the possible answer would be

a) set of all (u. v) such that u and v are ratios of p/q of integers.

b) set of all (u. v) where u=0 or v=0.

How can these vectors be closed for one and not closed for the other operation?