Communication is an Equivalence Relation. Show that i → j in S if and only if there are states i1,...,in ∈ S such that pi,i1 pi1,i2 ··· pin,j > 0. Show that the communication relation ↔ is an...

Communication is an Equivalence Relation. Show that i → j in S if and only if there are states i1,...,in ∈ S such that pi,i1 pi1,i2 ··· pin,j > 0. Show that the communication relation ↔ is an equivalence relation in that