Reply To: Complex "or' Rules

January 31, 2018 at 6:14 pm #45588
Mike Kim
Keymaster

Hi Immanuel,

Happy to try and help —

One small suggestion I have is to try using some physical items (toy cars would be great but anything will do) to visualize how these rules play out — may feel a little silly, but it can also be very helpful for helping your mind more easily “see” the consequences of these rules.

To begin, let’s quickly review the difference between just having “or” vs having “or…but not both.”

A statement like “J will arrive before M or N” could mean

a) J arrives before M but not N (meaning J arrives after N).
b) J arrives before N but not M (meaning J arrives after M).
c) J arrives before both M and N.

The only scenario that this sort of statement would exclude is

a) J arrives after both M and N.

Again, by its nature, an “or” statement could allow for the possibility of both.

In contrast, a statement like “J will arrive before M or N, but not both” means something more specific — exactly one of those consequences will be true, and the other will not be.

So, for this statement, we have two things that could be true:

a) J arrives before M

b) J arrives before N

And per this rule, what we know is that when one of those is true, the other one must be false — so, for

a) If J arrives before M, it must be after N.
b) If J arrives before N, it must be after M.

Hence, per this rule, “J will arrives before M or N, but not both,” the two ways it could play out are:

N – J – M or M – J – N, just as you said.

Okay, now let’s move on to a rule like “J will arrive after M or before N, but not both.”

Again, what we know is that in order to satisfy this rule, we must have one of the “or” items be true, and the other false.

So, it could be true that

a) J arrives after M

Or

b) J arrives before N.

Let’s play each of those out.

a) Per this rule, when J arrives after M, it cannot arrive before N — so that means that when J arrives after M, it must arrive after N.

b) Per this rule, when J arrives before N, it cannot arrives after M — so that means that when J arrives before N, it must arrive before M.

Thus, the two ways this rule can play out are that —

a) J arrives after both M and N or

b) J arrives before both N and M.

Very, very easy to get turned around, but I hope that helps clear things up, and if you have any follow-up please let me know —

Best,

Mike Kim