Step 1 :Given sets are: \(A = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}\) and \(B = \{3, 5, 7, 9, 11, 13\}\).
Step 2 :The union of two sets is a set containing all the elements of both sets. It's a combination of all the unique elements from both sets.
Step 3 :So, the union of sets A and B, \(A \cup B\), is \(\boxed{\{1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13\}}\).