Answer
a)Showing that there are at least nine freshmen, at least
nine sophomores, or at least nine juniors in the class.
b) Showing that there are either at least three freshmen, at
least 19 sophomores, or at least five juniors in the
class.
Work Step by Step
a) If there were fewer than 9 freshmen,
-fewer than 9 sophomores,
- and fewer than 9 juniors in the class,
- there would be no more than 8 with each of these
three class standings, for a total of at most 24 students,
contradicting
-the fact that there are 25 students in the class.
b) If
-there were fewer than 3 freshmen,
- fewer than 19 sophomores,
-and fewer than 5 juniors,
-then there would be at most 2 freshmen,
-at most 18 sophomores, and at most 4 juniors, for a total of at most 24 students.
-This contradicts the fact that there are 25 students in the class.
