NUMBER SET NOTATION AND LANGUAGE

Question

One year 37 students sat for physics,48 sat for chemistry and 45 sat for biology.15 students sat for physics and Chem,13 sat for Chem and bio,7 sat for physics and bio and 5 students sat for all 3 calculate n(P U C U B)

Answer 1

First, the notation n(P U C U B) represents the number of people who sat for physics OR chemistry OR biology.

We are given:

n(P) = 37

n(C) = 48

n(B) = 45

n(P ∩ C) = 15

n(C ∩ B) = 13

n(P ∩ B) = 7

n(P ∩ B ∩ C) = 5

By drawing a Venn diagram, we can see that we need to add up each of the categories, but then we need to subtract the parts where it interests twice for double counting and then add back where it intersects all three times.

Thus, n(P U C U B) = n(P) + n(C) + n(B) - n(P ∩ C) - n(C ∩ B) - n(P ∩ B) + n(P ∩ B ∩ C)

Plugging in the numbers given => 37 + 48 + 45 - 15 - 13 - 7 + 5

Hence, n(P U C U B) = 100