Question

Montgomery College has a 64-piece band and a 35-piece orchestra. If 14 people are members of both the band and the orchestra, can the band and orchestra travel in two 45-passenger buses?

Answer 1

Let U = {6, 7, 8, 9, 10, 11, 12}, A = {6, 7, 8, 9}, B = {6, 7, 10, 11}, and C = {8, 10, 12}. List all the members of the given set. (Enter your answers as a comma-separated list.)
(A ∪ B) ∩ C

Answer 2

64+35-14 = 86
So, two buses can hold the lot. Even chaperones!

(A ∪ B) = {6,7,8,9,10,11}
So,
(A ∪ B) ∩ C = {8,10}