Question

Am I correct in saying that this is true: {x} is an element of {x, {x}} ?

Answer 1

yes

Answer 2

Yep. Like pretend like we had the set {v,tunafish sandwich, {tunafish sandwich}}
v is an element of that set
tunafish sandwich is an element of that set
{tunafish sandwich} is an element of that set

but {v} is not an element of that set