The dog or the cat is …

The dogs or the cats are …

The dog or the cats are …

The dogs or the cat is ….

Here the subject is singular. So we use the singular verb. Only one of the subjects counts when using the conjunction “or”. If “and” were used, we would use the plural verb, “have.”

The teachers or the students have to (verb).

The subject “the teachers” is plural, as is “the students.” Therefore, even with the conjunction “or” this sentence requires the plural verb.

You or your son have to (verb).

In the case where the two parts of the subject do not have the same person or plurality, use the first part of the subject to determine the conjugation of the verb. “You have to (verb),” is unaltered by the addition of “or your son.”

The teachers or the students have to.

Isolate one of the subjects (“he”) and use the verb form for that.

for example, “He or she has/have to” would become

“He has to” or “She has to”

it works when i try it