When you want to combine two positive sentences, you will need so or too.
Example:
She walks to school every morning.
They walk to school every morning.
Eliptical sentences:
- She walks to school and they do too.
- She walks to school and so do they.
The patterns are:
... and + S + Auxiliary + too .
... and + so + Auxiliary + S .
When you want to combine two negative sentences, you will need either or neither.
Example:
She doesn't go to the office.
I don't go to the office.
Eliptical sentences:
- She doesn't go to the office and I don't either.
- She doesn't go to the office and neither do I.
The patterns are:
... and + S + Auxiliary + not + either .
... and + neither + Auxiliary + S .
P.S
You don't need to put 'NOT' when you use 'NEITHER' because neither stands for 'Not + Either'.