TITLE: What is the logical connective for Either.. Or?
QUESTION [6 upvotes]: I have a statement,

Either p or q

and I have to write it in terms of logical connectives but I don't get which logical connector should I be using?
Here is what I did (I think there could have been a better way to do this)

$(p \lor q ) \land (\neg((p \Rightarrow q) \land (q \Rightarrow p)))$

REPLY [2 votes]: There are several symbols for exclusive or, including $\oplus$ and $\veebar$. However, while in classical logic such connectives are both easily defined in terms of existing connectives and by means of a truth-table, they are not commonly employed in mathematics.
It's worth noting that there are many minimal functionally complete sets of logical connectives, but the definition of xor in terms of formulae using predefined connectives will be different in each. An obvious one is replacing $\phi \oplus \psi$ with $(\phi \vee \psi) \wedge \neg (\phi \wedge \psi)$.