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

Step 2 ：Find the complement of the union: \(n(A \cup B)^{\prime} = n(U) - n(A \cup B)\)

Step 3 ：Plug in the given values: \(n(A \cup B)^{\prime} = 20 - (12 + 9 - 4)\)

Step 4 ：Simplify the expression: \(n(A \cup B)^{\prime} = 20 - 17\)

Step 5 ：\(\boxed{n(A \cup B)^{\prime} = 3}\)