suppose r be an equivalence relation { (a,a), (a,b),(b,a),(b,c),(a,c),(c,b),(c,a)} nw for r^(-1) to be an equivalence relation (a,a) belongs to inverse r since (a,a) belongs to r . nw for symmetric relation (a,b) belongs to r (b,a) belongs to inverse r as well (a,b) also belong s to inverse r . similarly (b,a) and (a,c) belongs to inverse r hence (b,c) as well hence we can say inverse of r is also an equivalence relation .
