Some Congruences on a Transformation Semigroup

Let X be a set with |X|3,TX the full transformation semigroup on X.Let E be an equivalence relation on X and TE(X)=f∈TX:(x,y)∈E■(f(x),f(y))∈E the subsemigroup of TX determined by E.Denote T2(X)=f∈TE(X):|f(X)|≤2∪id,where id denotes the identity map on X.Then T2(X) is a subsemigroup of TE(X).Among other things,some congruences on the semigroup T2(X) are described.