Let A and B be subsets of a universal set U and suppose n(U) = 350, n(A) = 130, n(B) = 90, and n(A B) = 50.
Find the number of elements in the set.
n(Ac n B)
Sketch out the Venn Diagram.
You are looking for where everything outside of A connects with B.
So that is the stuff in B, that is not also in A
There is 90 total in B.
But you need to remove the 50 that are in both A and B.
That will give you your answer : )
So multiple 130 with 90 and 350?
To find the number of elements in the set Ac ∩ B, where Ac represents the complement of set A, we need to follow these steps:
Step 1: Find the number of elements in set A complement, denoted as n(Ac). We can calculate this by subtracting the number of elements in set A from the number of elements in the universal set: n(Ac) = n(U) - n(A).
n(Ac) = 350 - 130 = 220
Step 2: Find the number of elements in the intersection of A complement and B, denoted as n(Ac ∩ B). We can calculate this by subtracting the number of elements in the intersection of A and B from the number of elements in set A complement: n(Ac ∩ B) = n(Ac) - n(A ∩ B).
n(A ∩ B) = 50 (Given)
n(Ac ∩ B) = n(Ac) - n(A ∩ B) = 220 - 50 = 170
Therefore, the number of elements in the set Ac ∩ B is 170.