Answer should be b.
A professor can teach 0 course also.So professor don't have total participation and thus it will have partial participation.
Nothing is mentioned on courses,If they say every course is taught by some professor then it would have been total participation of course.But since it is not mentioned means course may or may not participate in relation.hence there is no total participation as both entities have partial participation.
I wont discuss cardinality here as it is not asked in question.
So,we need partial participation constraint and obvious key constraint.So b is correct here.