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

Or

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

Or

2) J will be before N

And, per the “but not both” part, we know that when one thing happens, the other can’t.

So,

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 —

MK