We define $x \leq y$ operation as '$x
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.