Sets $A$ and $B$ are subsets of the universal set $U$. These sets are defined as follows. \[ \begin{array}{l} U=\{k, q, s, x, y, z\} \\ A=\{s, z\} \\ B=\{q, s\} \end{array} \] Find the following sets. Write your answer in roster form or as $\varnothing$. (a) $(A \cup B)^{\prime}=$ b) $A^{\prime} \cap B=$

Step 1 ：Find the union of sets A and B, denoted as \(A \cup B\). This is the set of elements that are in A or B. So, \(A \cup B = \{s, z, q\}\)

Step 2 ：Find the complement of \(A \cup B\), denoted as \((A \cup B)^{\prime}\). This is the set of elements in the universal set U that are not in \(A \cup B\). So, \((A \cup B)^{\prime} = U - (A \cup B) = \{k, x, y\}\)

Step 3 ：\(\boxed{(A \cup B)^{\prime} = \{k, x, y\}}\)

Step 4 ：Find the complement of set A, denoted as \(A^{\prime}\). This is the set of elements in the universal set U that are not in A. So, \(A^{\prime} = U - A = \{k, q, x, y\}\)

Step 5 ：Find the intersection of sets \(A^{\prime}\) and B, denoted as \(A^{\prime} \cap B\). This is the set of elements that are in both \(A^{\prime}\) and B. So, \(A^{\prime} \cap B = \{q\}\)

Step 6 ：\(\boxed{A^{\prime} \cap B = \{q\}}\)