Step 1 :Given set \(\varepsilon = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}\)
Step 2 :Find square numbers in \(\varepsilon\): \(S = \{1, 4, 9\}\)
Step 3 :Find even numbers in \(\varepsilon\): \(E = \{2, 4, 6, 8, 10, 12\}\)
Step 4 :Complete the Venn diagram: Place square numbers in set \(S\), even numbers in set \(E\), and the intersection of sets \(S\) and \(E\) contains the number \(4\)
Step 5 :\(\boxed{\text{Final Answer: } S = \{1, 4, 9\}, E = \{2, 4, 6, 8, 10, 12\}}\)