$\mathcal{D}-$class in a semigroup is a union of $\mathcal{L}$-classes

Question

I am reviewing section 2.2 of fundamentals of semigroup theory at the beginning they say that "Each $\mathcal{D}$-class in a semigroup is a union of $\mathcal{L}$-classes and also a union of $\mathcal{R}$-class." This statement is telling us that if I take $a\in S$ then $D_{a}=R_{a}\cup L_{a}$? or as the union of which classes can we see $D_ {a}$?. I am somewhat confused about this and I appreciate any help!

Answer 1

No. A precise statement would be that $D_a$ is the union of all $R_b$ such that $a \mathrel{\cal L} b$, or the union of all $L_b$ such that $a \mathrel{\cal R} b$. See the famous "eggbox picture".