I'm confused what verb would concord in the following couple of sentences:
The number of students and the number of teachers are/is decreasing day by day in the school.
Either a number of teachers or a number of students is/are participating in the college's festival.
According to my understanding the number of is always followed by a singular verb even two the number of are joined with and. Also, a number is always followed by a plural verb. So I think the former will take is while the latter concord with are. But I'm not sure.