if $P(x, y)$ is the path predicate of any directed graph, then the predicate $P(x, y)\wedge P(y, x)$ is an equivalence relation. The equivalence classes of this relation are called strongly connected components. Prove that a graph has no strongly connected components with more than one element if and only if it has no directed cycle with more than one node.
I don't understand the part Prove that a graph has no strongly connected components with more than one element if and only if it has no directed cycle with more than one node.
if it's an equivalence class then it has equivalence classes so how can it have no strongly connected components ?