Exercise 1.

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

• F₁ = {x,(x + 1)y},
• F₂ = {x, xy},
• F₂ = {x², xy},
• F₃ = {y,(y + 1)x},
• F₅ = {x² - 4,(x - 2)y² + (x + 2)^y}

Among these sets, tell which one is a triangular set? a regular chain?

Answer 1