Question

If n (A) = 36, n (B) = 10, n (A∪B)=40, and n(A′)=27 find n(U) and n(A∩B).

Answer 1

Answer:

we have n(A') = 27 & n(A) = 27

since n(A') = n(U) - n(A)

therefore n(U) = n(A') + n(A)

n(U) = 27 + 36 = 63

now n(AUB) = n(A) + n(B) - n(A⋂B)

therefore n(A⋂B) = n(A) + n(B) - n(AUB)

n(A⋂B) = 36 + 10 - 40 = 6