For the universal set, \( U=\{g, h, p, q, r, x\} \), complete the parts below. Write your answers in roster form or as \( \varnothing \). (a) Suppose \( B=\{p, q, x\} \). Then what is \( \bar{B} \) ? \[ \bar{B}=\square \] (b) Suppose we know that \( \bar{C}=\{g, q, r, x\} \). Then what would \( C \) have to be? \( C=\square \)

Let's solve each part step by step using the universal set \( U = \{g, h, p, q, r, x\} \). ### (a) Finding \( \bar{B} \) Given: \[ B = \{p, q, x\} \] The complement of \( B \), denoted \( \bar{B} \), consists of all elements in \( U \) that are **not** in \( B \). \[ \bar{B} = U - B = \{g, h, p, q, r, x\} - \{p, q, x\} = \{g, h, r\} \] **Answer:** \[ \bar{B} = \{g, h, r\} \] ### (b) Finding \( C \) from \( \bar{C} \) Given: \[ \bar{C} = \{g, q, r, x\} \] To find \( C \), we take the complement of \( \bar{C} \), which means removing all elements of \( \bar{C} \) from \( U \). \[ C = U - \bar{C} = \{g, h, p, q, r, x\} - \{g, q, r, x\} = \{h, p\} \] **Answer:** \[ C = \{h, p\} \] **Final Answers:** - (a) \( \bar{B} = \{g, h, r\} \) - (b) \( C = \{h, p\} \)