Question

One year, 37 students sat an examination in Physics, 48 sat an examination in Chemistry and 45 sat an examination in Biology. 15 students sat examinations in Physics and Chemistry, 13 sat examinations in Chemistry and Biology, 7 sat examinations in Physics and Biology and 5 students sat examinations in all three. a Draw a Venn diagram to represent this information. b Calculaten n(P cup C cup B)

Answer 1

Answer:

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

Answer 2

Step-by-step explanation:

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