\( ( A \cup C ) ^ { C } \)

To solve the problem \(( A \cup C ) ^ { C}\), we need to find the complement of the union of sets \(A\) and \(C\). The complement of a set \(X\), denoted by \(X^C\), is the set of all elements in the universal set that are not in \(X\). Let's break down the steps to solve this: 1. **Union of Sets \(A\) and \(C\)**: First, we find the union of sets \(A\) and \(C\), denoted by \(A \cup C\). This is the set of all elements that are in \(A\), in \(C\), or in both. 2. **Complement of the Union**: Then, we find the complement of the union, denoted by \((A \cup C)^C\). This is the set of all elements in the universal set that are not in \(A \cup C\). Let's denote the universal set as \(U\). The complement of \(A \cup C\) can be written as: \[ (A \cup C)^C = U - (A \cup C) \] This means we take the universal set \(U\) and remove all the elements that are in \(A \cup C\). Without knowing the specific sets \(A\), \(C\), and the universal set \(U\), we cannot provide a numerical or specific set answer. However, the general form of the solution is: \[ (A \cup C)^C = U - (A \cup C) \] This expression represents the set of all elements in the universal set \(U\) that are not in the union of sets \(A\) and \(C\).