2
votes
1answer
29 views

Union of Cartesian squares

I am trying to find sufficient and necessary conditions for a relation to be representable as a union of Cartesian squares: $\bigcup_{i\in I}(X_i\times X_i)$ for some family $X_i$ of sets. One ...
1
vote
1answer
18 views

Validity of an inequality

Is this relation true ? $\Pi_{i=1}^n v_n \le \left(\frac{\sum_{i=1}^{n} v_n}{n}\right)^n$ Thank you
3
votes
1answer
130 views

About binary relations under certain conditions and their composition

(I have edited it. The previous version was with errors.) Let $A$ be a set. Let $\pi_0$, $\pi_1$ be projections from $A\times A$. Let $F_0$, $F_1$, $G_0$, $G_1$ be binary relations on $A$. Let ...
0
votes
1answer
218 views

Direct products in the category Rel

Please describe direct products in the category Rel.
-6
votes
1answer
207 views

Order of products and order of multipliers

I asked this question (and have received an answer) at MathOverflow. Now a little more difficult question: Let $f$ and $g$ are binary relations (on some set $\mho$). The function $f\times^{C} g$ is ...