The truth table for a logical disjunction shows that there is only one situation where the result can be false, being when both statements are false. As long as one statement is true, the result is also true.
This makes perfect sense to me, but I am wondering why this is the case. Could it not have been equally correct that the false would override the true. A true statement seems to have some governing power for no particular reason.
For example, given the propositions:
p.I play for a baseball team (Assigned to False)
q.I play for a soccer team (Assigned to True)
$$ p \lor q$$
would not be seen as a true or false compound statement in English, so what is the reasoning for this precedence in propositional logic?
Any help is greatly appreciated.