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??

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