(~x∧y)∨(x∧~y)
I thought about it and got a working expression on my second try. I got or(and(not(x),y),and(x,not(y)). Here’s the truth table:
Thinking about the operators as english statements helped.
I’m kind of confused what you’re asking here. The confusion is about “what universal sets can you make” and “what small set of set of operators have you discovered is universal”. Aren’t those the same thing?
To answer what I think you’re asking:
I also went ahead and made “and”, “not”, and “or” out of nor. Assuming that the set {and, or, not} is universal you can make that universal set out of the smaller universal set {nand, nor}.