quick "help!" question

[sicola at DOLPHIN.UPENN.EDU]

In my advanced grammar class, I've been working with my ESL students on
agreement with words like "neither" "either" "both" etc.

Some of them are having a hard time distinguishing and rationalizing the
differences between:

1.  "Neither Bob nor Joe studied." = Bob didn't and Joe didn't (either).
2.  "Either Bob or Joe didn't study." = One studied, the other didn't, we
don't know which one is which.
3.  "Both Bob and Joe didn't study." = Could have the same meaning as #1, OR
#2, ie: not BOTH, just one.

Can anyone more syntactically savvy help me with a more
logical/mathematical/graphic (and SIMPLE) representation of why this is the
case? The more I try to explain it, the more we go in circles and the more I
start to question my own name.

At this point, I'm not sure I even wrote these correctly in this e-mail!

Thanks to anyone who has the magic bullet...

Laura
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