Step 1 :Let \(U = \{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20\}\) and \(C = \{1,3,5,7,9,11,13,15,17,19\}\).
Step 2 :The set \(C^\prime\) is the complement of set \(C\) in \(U\). This means that \(C^\prime\) contains all the elements in \(U\) that are not in \(C\).
Step 3 :To find \(C^\prime\), we can subtract the elements of \(C\) from \(U\).
Step 4 :So, \(C^\prime = \{2, 4, 6, 8, 10, 12, 14, 16, 18, 20\}\).
Step 5 :Final Answer: \(\boxed{\{2, 4, 6, 8, 10, 12, 14, 16, 18, 20\}}\)