Is identity included in the "key" in predicate logic?

Question

So, my exam is in a few days. We've been told to practice setting up a key in predicate logic. . From what I've understood, a typical key looks something like this:

$ Lxy$: $x$ likes $y$

$Rx$: $x$ is rich

$j$: John

But, something my lecturer said about identity made me wonder whether or not I should include it in the key (if I am going to use identity, that is). He said that, for example, $x=y$ is the predicate $=xy$ ($x$ is identical to $y$, or something similar), only that since having the "$=$" in the middle is what we're used to (before logic), that's what we do in logic as well.

Thus, I have the impression that it is the same as a predicate (like "$Lxy$"), and therefore wonder whether I should have it in the key or not? If not, why not? :)

Thanks!

Answer 1

No need to include it in your key: it seems clear that your instructor accepts $x = y$ as denoting $=_{xy}\quad$

...having the "=" in the middle is what we're used to (before logic), that's what we do in logic as well.

So you are free to simply use "$x = y$" to denote $x = y$.