QuestionUse the given information to determine the number of elements in each of the four disjoint subsets in the following Venn diagram. $$\begin{array}{l} n(A)=30 \\ n(B)=50 \\ n(A \cup B)=70 \\ n(U)=200 \end{array}$$ a. $n\left(A \cap B^{\prime}\right)=$ $\square$

Studdy Solution
Calculate $n\left(A \cap B^{\prime}\right)$:
$$n\left(A \cap B^{\prime}\right) = n(A) - n(A \cap B)$$
Substitute the known values:
$$n\left(A \cap B^{\prime}\right) = 30 - 10$$ $$n\left(A \cap B^{\prime}\right) = 20$$
The number of elements in $A \cap B^{\prime}$ is:
$$\boxed{20}$$