## Separating a Group Into Equivalence Classes

The table represents a group of individuals and their their ability to send and receive messages.
 Can Send to\Can Receive From A B C D E F G H I J A 0 0 0 0 0 1 0 0 0 1 B 0 0 0 0 1 0 0 0 0 0 C 0 1 0 0 1 0 0 0 0 0 D 0 0 0 0 0 0 0 1 0 1 E 0 1 1 0 0 0 0 0 0 0 F 0 0 0 0 0 0 0 0 0 0 G 0 0 0 0 0 0 0 1 0 0 H 0 0 1 0 0 0 0 0 1 0 I 0 0 0 0 0 0 1 0 0 0 J 1 0 0 0 0 0 0 0 0 0
Obviously an individual can send a message to themselves. An individual can act as a relay to pass on a message. C cannot send a message to A directly, but he can send a message to J who can then send it to A. We can list the individuals and those they can send a message to, either directly or via some other individual.
 Can Send Message To Can Receive Message From A A, F, J A, D, J B B, C, E B, C, D, E, G, H, I C B, C, E B, C, D, E, G, H, I D A, B C, D, E, F, G, H, I, J D E B, C, E B, C, D, E, G, H, I F F A, D, F, J G B, C, E, G, H, I D, G, H, I H B, C, E, G, H, I D, G, H, I I B, C, E, G, H, I D, G, H, I J A, F, J A, D, J
The intersections of the 'send to' and 'receive from' sets gives the sets
$\left\{ \left\{ A, \; J \right\}, \; \left\{ B, \; C, \; E \right\}, \; \left\{ D \right\}, \; \left\{ F \right\}, \; \left\{ G, \; H, \; I \right\} \right\}$
.
These are the equivalency classes the the group of individuals.