Let A and B be subsets of a universal set U and suppose n(U) = 300, n(A) = 150, n(B) = 120, and n(A ∩ B) = 60. Compute:

Question

Let A and B be subsets of a universal set U and suppose n(U) = 300, n(A) = 150, n(B) = 120, and n(A ∩ B) = 60. Compute:

(a)     n(A^c ∩ B)

 

(b)     n(B^c)

 

(c)     n(A^c ∩ B^c)

Answer 1

a) n(A'B) = n(B) - n(AB) = 120 - 60 = 60

b) n(B') = n(U) - n(B) = 300 - 120 = 180

c) n(A'B') = n(U) - n(A) - n(A'B) = 300 - 150 - 60 = 90

Alternatively, n(A'B') = n(U) - n(A U B) = n(U) - (n(A) + n(B) - n(AB)) = n(U) + n(AB) - n(A) - n(B) = 300 + 60 - 120 - 150 = 90