Cardinals of all Generating Subsets in Semigroup of all Binary Relations on an Infinite set and Its Certain Subsemigroup

The following is proved: If X is an infinite set, S is a generating subedt of|R(X) (or |P(X), or |F(X), or Sym(X)), then|S|=2^|X|=exp(|X|), Where |R(X)=R: R⫅X²,|P(X)=f: f∈|R(X) & f is a function,|F(X)=f: f∈|P(X) & domain(f)=X, Sym(X)=φ: φ is a bijection on X.