UPSC NDA Math Model Paper 8

Given: n (U) = 1000, n (X) = 300, n (Y) = 400 and n (X ∩ Y) = 200
As we know that, n (X ∪ Y) = n (X) + n (Y) - n (X ∩ Y)
⇒ n (X ∪ Y) = 300 + 400 - 200 = 500
According to De-Morgans law : (X ∪ Y)’ = X ‘ ∩ Y’
⇒ n (X ∪ Y)’ = n (X ‘ ∩ Y’)
We know that, n (X ∪ Y)’ = n (U) - n (X ∪ Y)
⇒ n (X ∪ Y)’ = 1000 - 500 = 500
∴ n (X ‘ ∩ Y’) = 500