Sketch each of the following binary relations in the Cartesian plane and state if it is totally defined, and if it is well-defined:
(a) the binary relation $H = \{(x,y) \in \mathbb{R}× \mathbb{R}: xy=1 \}$
on $\mathbb{R}$;
(b) the binary relation $P$ on $\mathbb{R}_{\ge 0} × \mathbb{R}$ (where $\mathbb{R}_{\ge 0}$ is the set of non-negative real numbers) that is defined by specifying, for any $x \in \mathbb{R}_{\ge 0}$ and $y \in R$, that $$ x P y \iff x = y^2. $$
I'm given a question like this. What does the term "totally defined" mean? Does it mean total order relation?
And also what is the definition of a relation being "well defined"? I know the definition of a function being well defined but didn't know that any such restrictions were imposed on relation in general.
Please anyone have any idea what these two terms are saying, I'm just stuck there with the terms.