Question

There are 20 students in a chemistry class and 30 students in a physics class. find the number of students which are either in physics or in chemistry class in the following cases:

a)two classes meet at the same hour. (hint: n(C∩P) =Φ)

b)The two classes meet at different hours and 10 students are enrolled in both the courses. (hint: n(C∩P)=10)

Answer 1

We can answer these questions from Venn diagrams :

a) Two classes meet at the same hour :

n(C∩P) = n(C) + n(P)

n(C) = 20

n(P) = 30

= 20 + 30 = 50

b)when two classes meet differently

n(C∪P) = n(C) + n(P) - n(C∩P)

n (C∩P) = 10

= 20 + 30 - 10 = 40

Answer 2

a) 50                 b) 40

Let C be the set of the students in the chemistry class = 20 n(C) students

Let P be the set of the students in the physics class = 30 n(P) students

C ∩ P = ∅

n (C ∩  P) = 0

n (C U P) = n(C) +n(P) + n(C ∩  P)

= 20 + 30

= 50

(iii) n(C ∩  P) = 10

n(C ∩  F) = n(C) + n(F) - n(C ∩  P)

Substituting the values in this formula we get:

= 20 + 30 - 10

= 50 - 10

= 40