Negative Marks : -1 If wrong option is selected. Given $n(U)=20, n(A)=12, n(B)=9, n(A \cap B)=4$, where $U$ is universal set, $A \& B$ are subsets of $U$, then $\left(n(A \cup B)^{\prime}\right)$ equals :-

Step 1 ：Find the union of sets A and B using the formula: \(n(A \cup B) = n(A) + n(B) - n(A \cap B)\)

Step 2 ：Calculate the complement of the union by subtracting the result from the total number of elements in the universal set: \(n((A \cup B)') = n(U) - n(A \cup B)\)

Step 3 ：Plug in the given values: \(n(U) = 20, n(A) = 12, n(B) = 9, n(A \cap B) = 4\)

Step 4 ：Calculate the union: \(n(A \cup B) = 12 + 9 - 4 = 17\)

Step 5 ：Calculate the complement: \(n((A \cup B)') = 20 - 17 = 3\)

Step 6 ：\(\boxed{n((A \cup B)') = 3}\)