 Let \(E\) be an equivalence relation defined on a set \(A\). For \(x\) in \(A\), \([x]\) is the set of all \(y\) in \(A\) such that \(E(x, y)\); this is the equivalence class of x determined by E. The equivalence relation \(E\) divides the set \(A\) into mutually exclusive equivalence classes whose union is \(A\). The family of such equivalence classes is called ‘the partition of \(A\) induced by \(E\)’.