
About binary relations and their composition
Posted:
Sep 6, 2013 10:58 PM


> Let A be a set. > Let pi_0, pi_1 be projections from AxA. > Let F_0, F_1, G_0, G_1 be binary relations on A.
> Let phi_A be the maximal binary relation in (AxA) x (AxA) such that > pi_0 o phi_A subset F_0 o pi_0 and pi_1 o phi_A subset F_1 o pi_1.
I don't see how pi_0 and phi_A can compose as pi_0 subset AxA x A and phi_A subset AxA x AxA.
> Let phi_B be the maximal binary relation in (Ax > A)x(Ax A) such that pi_0 o phi_B subset > G_0 o pi_0 and pi_1 o phi_B subset G_1 o pi_1.
> Prove (or disprove) that Sigma=phi_B o phi_A is the maximal > binary relation on A such that pi_0 o Sigma subset G_0 o > F_0 o pi_0 and pi_1 o Sigm asubset G_1 o F_1 o pi_1.

