Argument against the existence of the exclusive "OR" in english. The book I'm reading says that the natural English sentence 
 (38) - Today is either Monday or Tuesday

is not an example of an exclusive "Or" in natural English. 
As I understand it, his argument goes like this: 
1- In order for an exclusive or to exist, it must exist the first row of its truth table, that is, it must be possible for A and B to be true. 
2- Since the statement (38) makes it impossible for A and B to be true, then the first row does not exist, then the exclusive or does not exist either. 
Is this a good argument? What happens to a statement in which some row is not possible to evaluate because the scenario is not possible? 

It's a terrible argument. 
First of all, the rows in a truth-table reflect the possible truth-values one could assign to the statements involved, where the whole point is that one does not look at the meaning of the atomic claims involved: a truth-functional analysis is just that: looking at how the truths of different statements relate to each other in terms of the truth-functional operators involved. So, given that there are no operators involved in either 'Today is Monday' and 'Today is Tuesday', a truth-functional analysis will simply treat these statements like two independent statements $P$ and $Q$', and thus under this analysis, it is possible for both statements to be true at the same time just fine. In fact, even a statement like $1=1$ will be treated as a single statement $P$, and therefore will be considered a statement that can be false under a truth-functional analysis. So you always have all possible rows for the truth-table, including the one where both statements are true, even if in our specific world the two statements cannot both be true. So this goes against claim 2.
Claim 1 makes even less sense: in order for there to be some logical connective there must exist certain rows in the truth-table?! No, logical connectives exist whether or not there is some kind of analysis in terms of truth-tables or not.
