If A and B are two sets such that n(A) = 23, n(b) = 37 and n(A – B)

1.	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» 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

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»

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