UPSC NDA Math Model Paper 7

Given: n (X) = 300, n (Y) = 400 and n (X ∪ Y) = 500
As we know that, for any two finite sets A and B, n (A ∪ B) = n (A) + n (B) - n (A ∩ B)
⇒ n (X ∪ Y) = n (X) + n (Y) - n (X ∩ Y)
⇒ 500 =300 + 400 - n (X ∩ Y)
⇒ n (X ∩ Y) = 200
As we know that, for any two finite sets A and B, n (A - B) = n (A) - n (A ∩ B)
⇒ n (X - Y) = n (X) - n (X ∩ Y) = 300 - 200 = 100