🚀 go-pugleaf

>Is Window 3 a operation system?
>  If yes, why it cannot boot a pc?
>  If not, why ms-dos can be run under it?

There's probably no good answer to that question.  The term "operating
system" was invented to describe software that comes from a rather
different tradition.  An operating system fits into an architecture
that involves a fairly clear layering between hardware, device
drivers, operating system, application software, etc.  For reasons
having to do with limited hardware resources, as well as historical
reasons that are harder to justify, typical PC systems do not have the
sort of layered architecture into which an operating system fits.
E.g. an application program like Kermit will directly manipulate the
serial interface and screen, which normally only a device driver is
allowed to do, and will do interrupt handling functions that a
operating system would normally do.

Windows, at least when running on a 386 processor, performs a number
of functions that an operating system would normally do.  But not all
of them.  It sort of "fills in the holes" in MS-DOS's operating system
functionality (though not all of them).  It is designed to work with
MS-DOS, not on the bare machine, which is why you can't boot it.

Note by the way that MS-DOS doesn't exactly run "under" Windows.
Windows can run the MS-DOS command processor in a window, but that's
basically an applications program.  Windows does depend upon some of
the more operating system-like portions of MS-DOS (though it replaces
others).

Things get even more interesting when you run Windows with QEMM.  Then
normal operating systems functionality is split among MS-DOS, QEMM,
Windows and (to some extent) applications programs.

So I'm not convinced that it's useful to try to figure out which piece
of software is the "operating system" on a PC running Windows.  OS/2
and Unix, both of which will run on the same software, are a different
question.  Both of them look a lot more like a traditional operating
system.