Neither, Nor, So

Hi Michael:

You lost your balance and so did Becky. OK
You didn't lose your balance and nor did Becky. No.
You didn't lose your balance and neither did Becky.
You lost your balance and neither did Becky. No
Neither you nor Becky lost their balance.

Thanks for correcting those examples. So as it appears the following is not correct:

When the first statement is positive then “Neither” is used to connect the two sentences.

I’m fed up with your nonsense and neither is he.

But when the first statement is negative then “nor” has to be used.

I don’t like you and nor does she.

Sorry, my edits were not minimal ones; there are other possibilities.

When the first statement is negative, you can use either and neither or nor as a conjunction to a second negative statement.
Strictly speaking, neither is short for not either, and nor is short for not or.

Example:

I don't like you. She doesn't lik

Thanks for your explanation. The last example however I feel needs a bit more explaining. Your sentence reads:
I'm fed up with his nonsense, but he is not.
Let's just tweak the example. Let's say there is this girl Becky, this guy Tim and Me. I'd like to say that I'm fed up with Becky's nonsense and this is the case also for Tim in one sentence starting with:
I'm fed up with her nonse

I'm fed up with her nonsense and Tim is too.
I'm fed up with her nonsense and so is Tim.

Regards,
A-s