Problema Solution
There are 35 students in art class and 57 students in dance class. Find the number of students who are either in art class or in dance class.
a)When two classes meet at different hours and 12 students are enrolled in both activities.
b) When two classes meet at the same hour.
Answer provided by our tutors
Let
A be the set of students in art class
B be the set of students in dance class
n(A) = 35
n(B) = 57
a) When 2 classes meet at different hours and n(A ∩ B) = 12 we have:
n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 35 + 57 - 12 = 80
b) When two classes meet at the same hour we have A∩B = ∅ that is n(A ∩ B) = 0 and
n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = n(A) + n(B) = 35 + 57 = 92