I found a counterexample to the following conjecture:

Conjecture $latex f\cap^{\mathsf{FCD}} g = f\cap g$ for every binary relations $latex f$ and $latex g$.

The counter-example is $latex f = {(=)}|_{\mho}$ and $latex g = \mho\times\mho \setminus f$. I proved $latex f \cap^{\mathsf{FCD}} g = {(=)} |_{\Omega}$ (where $latex \Omega$ is the Frechet filter object).

The proof of this equality is presented in Funcoids and Reloids online article, the section Some counter-examples.

I hope the above counter-example may probably serve also as a base for disproving some conjectures about relationships of funcoids and reloids.

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