We define $x \leq y$ operation as '$x<y \ \ or \ \ x=y$'. But this is false when both $x<y$ and $x=y$ as both can not be true at the same time. But I read text books that use this expression in their proofs.
Should not exclusive or be used for this ? Is not there a logic error by defining $\leq$ using only disjunction but not xor in math books.
if you look a truth table definition of P or Q when both are 1 result is 1. But the result is 0 here. So we can not classify this as or. but using or in set union is not like this.