I've been self studying abstract algebra from these notes. I've ran across the following Lemma:
The confusing part is that $X$ is a "any subset" not any "subgroup", and that the term "normal set" appeared in place where I expected "normal subgroup". The definition of a "normal set" has not been provided and I couldn't find it with a quick Googling.
So the question is
What is a "normal set" and why is the proof of that Lemma obvious ?