Hi Claudio —
Happy to try and help —
It’s useful to keep in mind that every “Or, but not both” rule actually gives us two rules that must be followed — one of the things must be true, and the other must be false.
So, if we have a rule like “John goes to Disneyland on Tuesday or Wednesday, but not both days” —
Per the first part of the rule, we know we have two options for what must be true:
1) John goes to Disneyland on Tuesday
2) John goes to Disneyland on Wednesday
And, per the “but not both” aspect, we know there are secondary consequences in each situation, namely —
1) if John goes on Tuesday, he can’t go on Wednesday.
2) if he goes on Wednesday, he can’t go on Tuesday.
Connecting this to our ordering rules —
If we have
“J will arrive after M or before N, but not both”
First, we know we have two options for something that must be true:
1) J will be after M
2) J will be before N
And, per the “but not both” part, we know that when one thing happens, the other can’t.
For 1), When J is after M, it cannot be before N (meaning it must be after N).
That gives us J after both M and N.
For 2), When J is before N, it cannot be after M (meaning it must be before M).
That gives us J before both N and M.
It’s really hard not to get turned around on these rules, but I hope that helps clear things up —