Victor Porton's Math Weblog

Conjecture about binary relations:

Let f and g are binary relations, g is a subset of f. If gg^-1 = fg^-1, then exists a set K such that g = f|_K.

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(The reverse implication is obvious.)

At first it looks like a very simple problem and probably it is really simple but I have spent already many hours trying to prove this theorem. (Aren't I found an idiot today?)

Finally, I have decided that it is wrong and tried to find a counter-example. For this I have wrote an Ada95 program.

It is not yet nor optimized for speed (current version 1.0 just stupidly enumerates all possible variants) nor checked for errors but for now my program has found that there are no counter-examples for relations up to 4x4 size. (Then it becomes slow.)

Can anybody prove or disprove this theorem?

It is important for my math logic and category theory research.

Tags: Math problems