I have the ideal: I:= {P ∈ ℚ [x,y] | P(5,0) = P(1,1) = 0}. Which I have proven is an ideal and now I am unsure how to answer the following questions.
1: Determine the variety V (I) associated with I. Justify your answer. 2: Give an example of a set S ⊂ ℚ such that V(I(S)) ≠ S.
Any help would be appreciated.