A proof by contradiction that there is no largest even integer begins: *'Suppose is the largest even integer.'* Which statement produces the contradiction?

Answer and explanation

Correct answer: E. is an even integer larger than

  1. Step 1: If is even then is also even and .
  2. Step 2: That contradicts the assumption that is the largest even integer, so no largest even integer exists.
Answer
is an even integer larger than .
Why not the others: is smaller and gives no contradiction; even is already assumed; is odd, so it does not compete with as an even integer; is larger than only when , so it does not give a general contradiction.

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