Step 1 :Let the universal set \(U = \{19, 20, 21, 22, 23, 24, 25\}\) and the set \(A = \{19, 23, 24, 25\}\).
Step 2 :The question is asking for the complement of set A in U. The complement of a set A, denoted by \(A^\prime\), is the set of all elements in the universal set U that are not in A.
Step 3 :So, we need to find all the elements in U that are not in A.
Step 4 :\(U = \{19, 20, 21, 22, 23, 24, 25\}\)
Step 5 :\(A = \{19, 23, 24, 25\}\)
Step 6 :\(A^\prime = \{20, 21, 22\}\)
Step 7 :Final Answer: \(A^\prime = \boxed{\{20, 21, 22\}}\)