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

Let's solve each part step by step. ### Part (a) **Given:** - Universal set \( U = \{f, g, h, p, q, r, x\} \) - Set \( A = \{f, g, q, r, x\} \) **Find \( A^{\prime} \) (the complement of \( A \)):** The complement of \( A \) consists of all elements in \( U \) that are not in \( A \). \[ A^{\prime} = U \setminus A = \{h, p\} \] ### Part (b) **Given:** - \( B^{\prime} = \{p, q, r\} \) **Find \( B \):** Since \( B^{\prime} \) is the complement of \( B \), \( B \) consists of all elements in \( U \) that are not in \( B^{\prime} \). \[ B = U \setminus B^{\prime} = \{f, g, h, x\} \] ### Final Answers (a) \( A^{\prime} = \{h, p\} \) (b) \( B = \{f,\, g,\, h,\, x\} \)