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1. A= ((x,y) [itex]\ni[/itex] R[itex]^{2}[/itex]/ x[itex]\geq[/itex]0)

I have many more questions like this, but since I cannot get the first one I think I might have a chance if I understand it.

As far as an attempt at an answer, I can only grasp that vector space must be commutative and associative and I can guess that this isn't the case because as y is negative x may become negative as well which would be outside the vector space, but how might I say that if if there are no determined operations on the set of (x,y) variables?

thank you!