
Originally Posted by
jenny,Mei
so the third sentence and the fourth sentence is not correct. right?
Have a look here, neither
nor. The Columbia Guide to Standard American English. 1993
Note that, if the person's intention is to express a multiple subject (e.g., Bill and John) separately, as two things, then it would be notionally awkward to use a singular verb. This is called notional agreement, a concept you might not find in most textbooks. Moreover, notional agreement is different from grammatical concord, which is what your teacher was talking about. Grammatical concord is the standard, whereas notional concord is just starting to catch on. 
Notional agreement
3. Neither Ireland nor Iceland are mountainous. 
4. Neither Bill Clinton nor John Major are film stars.
Grammatical concord
3. Neither Ireland nor Iceland is mountainous. 
4. Neither Bill Clinton nor John Major is a film stars.
Are your sentences correct? It depends on who you're asking.
From Subject-Verb Agreement
The pronouns
neither and
either are singular and require singular verbs even though they seem to be referring, in a sense, to two things.
- Neither of the two traffic lights is working.
- Which shirt do you want for Christmas?
Either is fine with me.
In informal writing,
neither and
either sometimes take a plural verb when these pronouns are followed by a prepositional phrase beginning with
of. This is particularly true of interrogative constructions: "
Have either of you two clowns read the assignment?" "
Are either of you taking this seriously?" Burchfield calls this "a clash between notional and actual agreement."*
Informal
1. Neither of you move. 
2. Neither of us have a driver's license. 
Formal
1. Neither of you moves. 
2. Neither of us has a driver's license. 
Does that help?