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

Let's solve each part step by step using the universal set \( U = \{h, p, q, r, x, y, z\} \). ### Part (a) **Given:** \( \overline{B} = \{p, x, y\} \) **To find:** \( B \) The complement of \( B \) (\( \overline{B} \)) consists of all elements in the universal set \( U \) that are **not** in \( B \). Therefore, to find \( B \), we subtract \( \overline{B} \) from \( U \): \[ B = U \setminus \overline{B} = \{h, p, q, r, x, y, z\} \setminus \{p, x, y\} = \{h, q, r, z\} \] **Answer:** \[ B = \{h, q, r, z\} \] ### Part (b) **Given:** \( C = \{p, q, r, x, y\} \) **To find:** \( \overline{C} \) The complement of \( C \) (\( \overline{C} \)) includes all elements in \( U \) that are **not** in \( C \). So, we subtract \( C \) from \( U \): \[ \overline{C} = U \setminus C = \{h, p, q, r, x, y, z\} \setminus \{p, q, r, x, y\} = \{h, z\} \] **Answer:** \[ \overline{C} = \{h, z\} \] ### Summary (a) \( B = \{h, q, r, z\} \) (b) \( \overline{C} = \{h, z\} \)