Number of Elements of union of two sets For the two subsets 𝐴 and 𝐵 of a universal set 𝑈, the following formula on the number of elements holds. That is 

Let 𝐴 and 𝐵 be two finite sets such that n(𝐴) = 15, n(𝐵) = 18, and n(𝐴 ∪ 𝐵) = 22; then find n(𝐴 ∩ 𝐵).

Given                                                                       Required 

n(A) = 15                                                                  n(A ∩ B) = ?

n(B) = 18

n(A ∪ B) = 22

We know that n(A ∪ B) = n(A) + n(B) - n(A ∩ B) 

From this n(A ∩ B) =  n(A) + n(B) - n(A ∪ B) = 15 + 18 - 22 = 33 - 22 = 11

So  n(A ∩ B) = 11

1. Let 𝐴 and 𝐵 be two finite sets such that n(𝐴) = 34, n(𝐵) = 46 and n(𝐴 ∪ 𝐵) = 70. Then, find n(𝐴 ∩ 𝐵). 

Given                                             Required 

n(A) = 34                                  number of people drinks both n(A ∩ B) = ?

n(B) = 46

n(A ∪ B) = 70

We know that n(A ∪ B) = n(A) + n(B) - n(A ∩ B) 

From this n(A ∩ B) =  n(A) + n(B) - n(A ∪ B) = 34 + 46 - 70 = 80 - 70 = 10

So  n(A ∩ B) = 10

2.There are 60 people attending a meeting.42 of them drink tea and 27 drink coffee. If every person in the meeting drinks at least one of the two drinks, find the number of people who drink both tea and coffee. (Hint: Use a Venn diagram).

Given                                             Required 

Let us say                                number of people drinks both n(A ∩ B) = ?

n(A) = number of people that drink tea = 42

n(B) = number of people that drink coffee = 27

n(A ∪ B) = 60

We know that n(A ∪ B) = n(A) + n(B) - n(A ∩ B) 

From this n(A ∩ B) =  n(A) + n(B) - n(A ∪ B) = 42 + 27 - 60 = 69 - 60 = 9

So  n(A ∩ B) = 9 ,........number of people who drinks both coffee and tea 





Last modified: Sanbata, 4 Onkoloolessa 2025, 8:37 AM