This conditional statement is evaluated as true (by the program Tarski's world) however it seems false could you help detect my mistake?

Question

So the way I read the statement is: there is an object x such that if it's a cube then it is between a and b. However, there is a cube but it is not between a and b, making the statement false. The exercise this came from started with "Common mistakes" so I'm assuming my assertion that this should be false is a common mistake.

Answer 1

So the way I read the statement is: there is an object x such that if it's a cube then it is between a and b. However, there is a cube but it is not between a and b, making the statement false.

It does not say "There is a cube between a and b".

It says "There is something that is between a and b if that object is a cube." Objects that are not cubes may satisfy this.

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Recall implication equivalence. So $\exists x~(\operatorname{Cube}(x)\to\operatorname{Between}(x,a,b))$ is equivalent to: $$\exists x~(\lnot\operatorname{Cube}(x)\vee\operatorname{Between}(x,a,b))$$

"There is something that is not a cube or is between a and b".

Any of the three dodecahedrons will serve as a witness that this is true.

Answer 2

This statement is indeed true.

To see this, we let $x$ be the dodecahedron which is between $a$ and $b$. Because $x$ is not a cube, it is trivially true that $cube(x) \to Between(x, a, b)$.