Use the union rule to answer the question.
If $n(B)=13, n(A \cap B)=4$ and $n(A \cup B)=33$, what is $n(A) ?$

Step 1 ：Given that the number of elements in set B, denoted as \(n(B)\), is 13, the number of elements in the intersection of sets A and B, denoted as \(n(A \cap B)\), is 4, and the number of elements in the union of sets A and B, denoted as \(n(A \cup B)\), is 33.

Step 2 ：We are asked to find the number of elements in set A, denoted as \(n(A)\).

Step 3 ：We can use the union rule, which states that \(n(A \cup B) = n(A) + n(B) - n(A \cap B)\).

Step 4 ：Rearranging this formula to solve for \(n(A)\), we get \(n(A) = n(A \cup B) - n(B) + n(A \cap B)\).

Step 5 ：Substituting the given values into this formula, we get \(n(A) = 33 - 13 + 4\).

Step 6 ：Simplifying this, we find that \(n(A) = 24\).

Step 7 ：So, the number of elements in set A is \(\boxed{24}\).