With "ni...ni" and "ou", the verb goes into the plural if both subjects can perform the action together. It stays singular if only one of them can perform it (exclusion). With "comme" and "ainsi que": plural if it is an addition, singular if it is a comparison.
Both subjects can act together: plural. Only one acts: singular.
Examples
Ni Paul ni Marie ne viendront.
Key word(s): viendront
Both of them can come (or not), so the plural.
Le chat ou le chien a renversé le vase.
Key word(s): a renversé
Only one of the two did the action, so the singular.
Le père, ainsi que le fils, est grand.
Key word(s): est
"Ainsi que" used as a comparison (set off by commas), so the singular.
Le père ainsi que le fils sont venus.
Key word(s): sont venus
"Ainsi que" used as an addition (no commas), so the plural.
Ni l'un ni l'autre ne sait.
Key word(s): sait
Neither of the two knows, so the singular (the plural is also accepted).
Common mistakes
Always using the plural after "ni...ni"
Forgetting that "ou" can express exclusion (and so take the singular)
Not seeing the difference between "ainsi que" as a comparison and as an addition
Test yourself
Ni toi ni moi ne ___ la réponse.
Ni toi (second person) ni moi (first person), so "nous savons" (plural, the first person wins).
Pierre ou Paul ___ élu président.
Only one can be elected, so the singular (exclusion).
Le courage, comme la patience, ___ une vertu.
A comparison (set off by commas), so the singular.
Tips to remember
Ask yourself: do the two subjects act together, or only one of them?
"Ainsi que" set off by commas means a comparison (singular). Without commas it means an addition (plural).
With "ni...ni" plus different persons, the lower person wins (moi > toi > lui).
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