Communication is an Equivalence Relation. Show that i $->$ j in Sifandonlyiftherearestatesi $,...,$i in Ssuchthatp p $$p $>0.$

$1$ n i$,$i$1$ i$1,$i$2$ in$,$j Show that the communication relation $$ is an equivalence relation in that it satisfies the following properties.

Reflexive: i $$ i$,$ i in S$.$

Symmetric: i $$ j if and only if j $$ i$,$ i$,$ j in S$.$ Transitive: If i $$ j and j $$ k$,$ then i $$ k$,$ i$,$j$,$k in S$.$