Question

Given n(U) = 32, n(A) = 20, n(AB) = 9, n(B') = 16 , what is the value of n(B)?

a. 9
b. 12
c. 16
d. 23

Answer 1

To find the number of elements in set B (n(B)), subtract the number of elements not in B (n(B')) from the total number of elements in the universal set (n(U)). Thus, n(B) = 32 - 16, which equals 16.

Step-by-step explanation:

Let's solve for the number of elements in set B, denoted as n(B). Given that n(U) = 32, n(A) = 20, n(AB) = 9, and n(B') = 16 (where B' is the complement of B), we want to find the value of n(B). Note that n(B') is the number of elements not in B, so n(B) = n(U) - n(B'). Plugging in the given values:

n(B) = 32 - 16 = 16

The value of n(B) is therefore 16, which corresponds to option c.