For you two: The IBM PC was the first PC and had a 8088 CPU. OS/2 and Xenix were for the 286 and up.
If you make virtual memory a necessary attribute to qualify as OS, there were no OS for the original IBM PC as the 8088 had no support for virtual memory. That's why my (tricky) question.
No. Xenix through at least version 2.1 ran on the original IBM PC (and early Xenix was ported to the 68000 (e.g. Tandy model 16), which also lacked hardware VM support).[1] You could also run IBM PC Unix in the form of Venix from Venturecom (Version 7 with some BSD things) and PC/IX from ISC (System III). Both were 'official' licensed Unix ports. In the Unix-ish camp, there was Coherent and Minix, as well as various MMU-less Linux projects (e.g. ELKS). And there are many interesting oddballs like iRMX.
Yes, OS/2 did require a 286 until it required a 386.
If you make virtual memory a necessary attribute to qualify as OS
That would be pedantic and historically inaccurate and we shouldn't engage in that.
If we are being pedantic then what you’re describing are called IBM-compatible PCs. Ie they weren’t made by IBM but were designed to support most other of the same software.
If what you're referring to as the "IBM PC" is the classic model 5150 and we follow your arbitrary designation of a "real OS", than no. But, by that same logic, I can say ducks aren't birds "if we consider birds only those with non-webbed feet".
If you make virtual memory a necessary attribute to qualify as OS, there were no OS for the original IBM PC as the 8088 had no support for virtual memory. That's why my (tricky) question.