Exercise 2.

We consider the following subsets of $\mbox{${\mathbb Q}$}$[x, y] where x < y holds.

• F₁ = {x - 1, y - 2}
• F₂ = {x(x - 1),(x - 1)y + 1}
• F₃ = {x(x - 1),(x - 1)y}
• F₄ = {x, xy + 1}
• F₅ = {x(y - 1) + (x - 1)(y - 2)y, xy + (x - 1)(y - 3)y}.

For each of them give a triangular decomposition of $\bf V$(F). In each case this will be a sequence of 0, 1 or 2 triangular sets such that the union of their regular zeros is $\bf V$(F).

Answer 2