Here is a possibility with stackengine and the \bigovoid symbol from mathabx (without replacing the default maths fonts with the mathabx fonts):
You can use a scaled up version of \bigcirc and \ooalign:
You can use TikZ to draw a circle node with a # inside. Using \DeclareMathOperator from amsmath improves the spacing. The character should be a bit smaller than the current font, which you can do using \smaller from the relsize package, to make sure it works in different fontsizes.
I have created your symbol with a combination of packages. Excuse me for the complicated code. The symbol has the name \disj. It is a variable name that you can change. Here is my MWE:
The not so short answer, where the code turned out to be longer than in my head. The code may look a bit cumbersome, but I did not optimise it in any way. I just wanted to show a solution where the input is interpreted and a truthtable is generated e.g. (A\oplus B)' as A XOR B and the result is negated. The code does not except every possible inputs. For ...
This is something quickly written. Does not steer the Mars rover, in fact it is just a one-liner. If you make your code copyable I will add all the table options, if needed. (In fact, I made zero efforts to make the output "pretty", nor to suppress spaces or empty lines.) Also one can use a loop to create all the rows. I added explanations to the output.