What does $\forall x (Triangle(x) \iff \exists y (Square(y) \land AboveOf(x,y)))$ imply?

44 Views Asked by At

I'm trying to make a Tarski World for this structure:

$$\forall x (Triangle(x) \iff \exists y (Square(y) \land AboveOf(x,y)))$$

I think that it means the following:

  • Element is a triangle if and only if there is a square below it. So every triangle must have squares below it.
  • There is a square that is below some element if and only if that element is a triangle. So no square should be below any elements that are not triangles.

However, the answer has a picture that has one square above the other. Why is that?