Question

If A and B are two sets such that n(A) = 23, n(b) = 37 and n(A – B) = 8 then find n(A ∪ B).

Hint n(A) = n(A – B) + n(A ∩ B) n(A ∩ B) = (23 – 8) = 15.

Answer 1

Given: n(A) = 23, n(B) = 37, n(A – B) = 8 

Using the hint 

n(A) = n(A – B) + n(A ∩ B) 

⇒ 23 = 8 + n(A ∩ B) 

⇒ n(A ∩ B) = 23 – 8 

⇒ n(A ∩ B) = 15

Visualizing the hint given, 

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

⇒ n(A ∪ B) = 23 + 37 – 15 

⇒ n(A ∪ B) = 45 

Hence n(A ∪ B) = 45