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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

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  1. 20 May, 00:19
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    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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