I was having a really difficult time with this as well, but then something stared to click for me. Hopefully I can explain it properly.

When dealing with an 'or' rule, we need to have at least one of the options included... so, for example:

/J -> F

/J, then we must select F to have one of the options included.

J, then we are free to included F or /F, because we have already included one of our options, the other one may join, or not - the rule floats away

/F, then we must include J to have one of our options included.

F, then we are free to included J or /J, because we have already included one of our options, the other one may join, or not - the rule floats away.

For the 'not both' rule, we can only have up to one of the options included...

So, for example:

J -> /F

J, then we must select /F, as we have no more room to fit F

/J, then we may select F or /F, as we can either fill it, or leave it empty - our rule floats away

F, then we must select /J, as we have no more room to fit J

/F, then we may select F or /F, as we can either fill it or leave it empty - our rules floats away.

I think the biggest breakthrough for me was that 'or' rules imply a minimum of one, while 'not both' implies a maximum of one.

Hopefully that was of some help - if not, Sorry!