"either of which" vs. "both of which"

[Hirobo]

Hi folks,

My assumptions are, that following sentences are grammatically
correct:
ex 1. There are A and B, both of which shall be new.
ex 2. There is A or B, either of which shall be new.

However, followings are not correct:
ex 3. There are A and B, either of which shall be new.
ex 2. There is A or B, both of which shall be new.

Are theare any grammatical rules like above?
Are my assumptions correct?

Thanks in advance for your help.

[Alan]

Although none of your sentences are natural, they are all structurally possible.
This is essentially an issue of sense/semantics rather than of grammar.