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We consider the following subsets of
[x, y] where x < y holds.

F_{1} = {x,(x + 1)y},

F_{2} = {x, xy},

F_{2} = {x^{2}, xy},

F_{3} = {y,(y + 1)x},

F_{5} = {x^{2}  4,(x  2)y^{2} + (x + 2)^{y}}
Among these sets, tell which one is a triangular set? a regular chain?
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Marc Moreno Maza
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