Find $A^{\prime} \cap B^{\prime}$ using roster method. \[ \begin{array}{l} U=\{1,2,3,4,5,6,7\} \\ A=\{1,3,5,7\} \\ B=\{2,5,7\} \end{array} \] Find $A^{\prime} \cap B^{\prime}$ using roster method. Be sure to include braces as needed. If necessary, use proper notation for the empty set. \[ A^{\prime} \cap B^{\prime}= \]

Step 1 ：The universal set U is \(U = \{1, 2, 3, 4, 5, 6, 7\}\)

Step 2 ：Set A is \(A = \{1, 3, 5, 7\}\)

Step 3 ：Set B is \(B = \{2, 5, 7\}\)

Step 4 ：The complement of set A, denoted by A', is the set of all elements in the universal set U that are not in A. So, \(A' = \{2, 4, 6\}\)

Step 5 ：The complement of set B, denoted by B', is the set of all elements in the universal set U that are not in B. So, \(B' = \{1, 3, 4, 6\}\)

Step 6 ：The intersection of two sets, denoted by ∩, is the set of all elements that are common to both sets. So, the intersection of the complements of sets A and B is \(A' \cap B' = \{4, 6\}\)

Step 7 ：Final Answer: \(\boxed{\{4, 6\}}\)