Predicate logic, transitivity (sort of?) I have a question. It involves 2 pictures for which I'm supposed to write a formula which is true for one, but false for the other.
The pictures can be found here on page 23 (the arrows pointing in a square)
Or you can find just the question and the squares here
My answer would be this:
$$\exists x \exists z (\forall y (Rxy \wedge Ryz)\rightarrow Rxz)$$
With $R$ being "$x$ has a relation to $y$".
Which is similar to transitivity. Would that be correct?
Thanks in advance, Rope.
P.S. Again sorry for asking so many questions, but I don't have the answers to these questions as it is a selfstudy.

I think we must have :

$(∃x)(∃y)(∃z)[\quad ¬(x = y) ∧ ¬(x = z) ∧ ¬(y = z) ∧ R(x, y) ∧ R(x, z)] \land (\forall w)(¬(w = y) ∧ ¬(w = z) ∧ ¬(y = z) ∧ R(w, y) ∧ R(w, z) \rightarrow (x = w)) \quad ]$

