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A student was asked to prove the statement: "If \(n\) is an odd integer, then \(n+1\) is an even integer."Below is the Student's Proof Attempt.
  1. Assume \(n\) is an even integer.
  2. By definition, there exists an integer \(k\) such that \(n=2k\).
  3. Then \(n+1 =2k+1= 2(k+1)\).
  4. Therefore, \(n+1\) is an even integer.
Identify the errors in the student's reasoning and write a correct version.
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