Use the given information to fill in the number of elements for each region in the Venn diagram.
\[
\begin{array}{l}
n(A)=16, n(B)=15 \\
n(A \cap B)=11, n\left(A^{\prime}\right)=32
\end{array}
\]
The number in place of $x$ should be $\square$.
- The number of elements not in A or B is \(\boxed{27}\).
Step 1 :Given that the total number of elements in set A, denoted as \(n(A)\), is 16 and in set B, denoted as \(n(B)\), is 15.
Step 2 :The number of elements in the intersection of A and B, denoted as \(n(A \cap B)\), is 11.
Step 3 :The number of elements not in A, denoted as \(n(A')\), is 32.
Step 4 :The number of elements in A but not in B is given by \(n(A) - n(A \cap B)\), which is \(16 - 11 = 5\).
Step 5 :The number of elements in B but not in A is given by \(n(B) - n(A \cap B)\), which is \(15 - 11 = 4\).
Step 6 :The number of elements in both A and B is given by \(n(A \cap B)\), which is 11.
Step 7 :The number of elements not in A or B is given by \(n(A') - (n(A) - n(A \cap B))\), which is \(32 - (16 - 11) = 27\).
Step 8 :Final Answer: The number of elements in each region of the Venn diagram is as follows:
Step 9 :- The number of elements in A but not in B is \(\boxed{5}\).
Step 10 :- The number of elements in B but not in A is \(\boxed{4}\).
Step 11 :- The number of elements in both A and B is \(\boxed{11}\).
Step 12 :- The number of elements not in A or B is \(\boxed{27}\).