Question

Assume that n(U) = 55,

n(A' B') = 11, n(
AB) = 13, and n(A n B') = 11. Find the following.
(1) n(An B)
(2) n(AUB)

Answer 1

Using the inclusion-exclusion principle, n(An B) is 13 and n(AUB) is 11.

Step-by-step explanation:

To find n(An B), we can use the inclusion-exclusion principle. The inclusion-exclusion principle states that:

n(An B) = n(A) + n(B) - n(AUB)

Given that n(A' B') = 11, n(AB) = 13, and n(A n B') = 11, we can substitute the values into the formula:

n(An B) = n(A) + n(B) - n(AUB)

= n(AB) + n(A' B') - n(A n B')

= 13 + 11 - 11

= 13

To find n(AUB), we can use the formula:

n(AUB) = n(A) + n(B) - n(An B)

Substituting the given values:

n(AUB) = n(A) + n(B) - n(An B)

= n(AB) + n(A' B') - n(An B)

= 13 + 11 - 13

= 11