For the universal set, \( U=\{4,5,6,7,8,9\} \), complete the parts below. Write your answers in roster form or as \( \varnothing \). (a) Suppose we know that \( A^{\prime}=\{4,6\} \). Then what would \( A \) have to be? \[ A=\square \] (b) Suppose \( B=\{5,6,7,8,9\} \). Then what is \( B^{\prime} \) ? \[ B^{\prime}=\square \]

Let's solve each part step by step. **Given:** - Universal set \( U = \{4,5,6,7,8,9\} \) ### (a) Finding \( A \) when \( A' = \{4,6\} \) - \( A' \) represents the complement of \( A \) with respect to \( U \). - To find \( A \), subtract \( A' \) from \( U \): \[ A = U \setminus A' = \{4,5,6,7,8,9\} \setminus \{4,6\} = \{5,7,8,9\} \] **Answer:** \[ A = \{5,7,8,9\} \] ### (b) Finding \( B' \) when \( B = \{5,6,7,8,9\} \) - \( B' \) represents the complement of \( B \) with respect to \( U \). - To find \( B' \), subtract \( B \) from \( U \): \[ B' = U \setminus B = \{4,5,6,7,8,9\} \setminus \{5,6,7,8,9\} = \{4\} \] **Answer:** \[ B' = \{4\} \] --- **Final Answers:** (a) \( A = \{5,7,8,9\} \) (b) \( B^{\prime} = \{4\} \)