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.