what is the relationship between X11 and gnome? [closed]

Is there a relationship between X11 and gnome ?

Yes

Does the gnome uses the X11 interface to display ?

Yes¹

or does the gnome implements some functionality that the X11 requires ?

Gnome implement functionalities users expect/require. X11 doesn't require Gnome, Gnome requires X11¹.

X11 is

1. a client/server network protocol allowing remote access to displays, keyboards and mice.
2. a low level API implementing the X11 protocol used to develop graphic applications
3. a library (libX11) implementing this API
4. a set of packages (servers, toolkits, applications, window managers, ...) using the X11 API, directly and/or through a toolkit.

Gnome is

1. a collection of applications based on the GTK+ toolkit, which itself uses the X11 API. These applications form a graphic environment including plenty of applications, window manager(s), accessories, ...

There are many other graphic environment, KDE based on the Qt toolkit being one of the well known competitor.

Before KDE and Gnome (read in the nineties), one of the most popular desktop environments was CDE, based on the Motif toolkit.

¹ Note that it is possible to select alternative underlying graphic layers with GTK+ 3. In such case, you might replace all occurrences of X11 in the first part of my reply by the back-end selected, e.g. Wayland, Quartz, Win32...

The relationship/dependencies remains the same.