Let A and B be subsets of a universal set U and suppose n(U) = 350, n(A) = 115, n(B) = 80, and n(A B) = 50.
Find the number of elements in the set.
n(Ac B)
To find the number of elements in the set n(Ac B), where Ac represents the complement of A, we need to first find the number of elements in A and then subtract it from the number of elements in A B.
Given the following information:
n(U) = 350 (total number of elements in the universal set U)
n(A) = 115 (number of elements in set A)
n(B) = 80 (number of elements in set B)
n(A B) = 50 (number of elements in the intersection of sets A and B)
To find n(Ac), the complement of A, we subtract the number of elements in A from the total number of elements in U:
n(Ac) = n(U) - n(A)
n(Ac) = 350 - 115
n(Ac) = 235
Now, to find n(Ac B), we calculate the number of elements in the intersection of sets Ac and B:
n(Ac B) = n(B) - n(A B)
n(Ac B) = 80 - 50
n(Ac B) = 30
Therefore, the number of elements in the set n(Ac B) is 30.