In propositional logic the order of precedence I have found for the logical connectives is
- $\neg$
- $\land$
- $\lor$
- $\Rightarrow$
- $\Leftrightarrow$
Where do I have to put the exclusive or $\dot\lor$ in the above list?
Note: I also asked this question on this the German forum matheboard.de two days ago. Because I did not get an answer there and because I also did not find an answer in the internet, I also want to ask this question here. I hope, this is okay.
Best Answer
The exclusive-or can be thought of as "compound connective": a connective that involves $\lor$, $\land$ and $\lnot$ in any one of its forms: $$p \dot\lor q \equiv (p \lor q) \land \lnot(p \land q)\equiv (p \lor q)\land (\lnot p \lor \lnot q) \equiv (p \land \lnot q) \lor (\lnot p \land q)$$
Then the table of precedence you've posted covers exclusive-or, implicitly at least, as can be seen in the "expanded" versions of the exclusive-or.