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
- Step 1: If is even then is also even and .
- 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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