Set \( B \) and the universal set \( U \) are defined as follows. \[ \begin{array}{l}U=\{h, p, q, r, x, y\} \\ B=\{h, q, y\}\end{array} \] Find the following sets. Write your answer in roster form or as \( \varnothing \). (a) \( B \cap B^{\prime}=\square \) (b) \( B \cup U=\square \)

To solve for the sets: (a) The complement of set \( B \), denoted \( B' \), includes all elements in the universal set \( U \) that are not in \( B \). Since \( B = \{h, q, y\} \), we can find \( B' \) as follows: \( B' = U - B = \{p, r, x\} \) Now, the intersection of \( B \) and \( B' \) is calculated: \( B \cap B' = \{h, q, y\} \cap \{p, r, x\} = \varnothing \) So, \( B \cap B' = \varnothing \). (b) The union of sets \( B \) and \( U \) combines all elements from both sets without duplication: \( B \cup U = \{h, q, y\} \cup \{h, p, q, r, x, y\} = \{h, p, q, r, x, y\} \) Thus, \( B \cup U = U = \{h, p, q, r, x, y\} \).