Use the given information to complete the following table.
\[
\begin{array}{l}
n(A)=40, n(B)=60 \\
n(A \cup B)=85, n(U)=110
\end{array}
\]
\begin{tabular}{lllc}
& A & A $^{\prime}$ & Totals \\
\hline B & $?$ & $?$ & $?$ \\
$\mathrm{~B}^{\prime}$ & $?$ & $?$ & $?$ \\
Totals & $?$ & $?$ & $?$
\end{tabular}
B' $^{\prime}$
Totals

Step 1 ：The given information tells us the number of elements in set A, set B, the union of sets A and B, and the universal set U. We can use these numbers to fill in the table.

Step 2 ：The intersection of sets A and B can be found by adding the number of elements in A and B and subtracting the number of elements in the union of A and B. This gives us \(n(A \cap B) = n(A) + n(B) - n(A \cup B) = 40 + 60 - 85 = 15\).

Step 3 ：The number of elements in the complement of A (A') can be found by subtracting the number of elements in A from the number of elements in the universal set. This gives us \(n(A') = n(U) - n(A) = 110 - 40 = 70\).

Step 4 ：The number of elements in the complement of B (B') can be found by subtracting the number of elements in B from the number of elements in the universal set. This gives us \(n(B') = n(U) - n(B) = 110 - 60 = 50\).

Step 5 ：The intersection of sets A and B' can be found by subtracting the intersection of A and B from the number of elements in A. This gives us \(n(A \cap B') = n(A) - n(A \cap B) = 40 - 15 = 25\).

Step 6 ：The intersection of sets A' and B can be found by subtracting the intersection of A and B from the number of elements in B. This gives us \(n(A' \cap B) = n(B) - n(A \cap B) = 60 - 15 = 45\).

Step 7 ：The intersection of sets A' and B' can be found by subtracting the number of elements in A, B, and the intersection of A and B from the number of elements in the universal set. This gives us \(n(A' \cap B') = n(U) - n(A) - n(B) - n(A \cap B) = 110 - 40 - 60 - 15 = -5\).

Step 8 ：The total number of elements in A, B, A', and B' can be found by adding the respective intersections. This gives us total_A = 40, total_B = 60, total_A_prime = 70, total_B_prime = 50, and total = 110.

Step 9 ：The intersection of A' and B' is negative, which is not possible. This suggests that there might be an error in the given information or in my calculations. Let's check the calculations again.

Step 10 ：After checking the calculations again, we find that the intersection of A' and B' should be \(n(A' \cap B') = n(U) - n(A \cup B) = 110 - 85 = 25\).

Step 11 ：\(\boxed{\text{Final Answer: The completed table is as follows:}}\)

Step 12 ：\[\begin{array}{lcccc}& A & A' & Totals \\hline B & 15 & 45 & 60 \B' & 25 & 25 & 50 \\hline Totals & 40 & 70 & 110\end{array}\]