Let \[ \begin{array}{l} U=\{a, f, g, m, q, s, u, z\} \\ A=\{a, u, z\} \\ C=\{f, g, m, q, s\} \end{array} \] Find $A \cup C^{\prime}$

Step 1 ：Given the universal set U = \{a, f, g, m, q, s, u, z\}, set A = \{a, u, z\}, and set C = \{f, g, m, q, s\}.

Step 2 ：The complement of a set is the set of all elements in the universal set that are not in the given set. So, we first find the complement of C in the universal set U.

Step 3 ：The complement of C in the universal set U is \{a, u, z\}.

Step 4 ：We are asked to find the set \(A \cup C^{\prime}\). This represents the union of set A and the complement of set C.

Step 5 ：The union of two sets is the set of all elements that are in either set. So, we find the union of A and the complement of C.

Step 6 ：The union of A and the complement of C is \{a, u, z\}.

Step 7 ：So, \(A \cup C^{\prime}\) = \{a, u, z\}.

Step 8 ：Final Answer: \(\boxed{\{a, u, z\}}\)