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(10 points) Find the mistake(s) in the following "proof by mathematical induction: Theorem: For all integers n 2 1, 3n-2 is even. "Proof (by mathematical induction): Suppose the theorem is true for an integer k, where k2 1. That is, suppose that 3k - 2 is even. We must show that 3k+1-2 is even. But 3k+1-2 3 3-2 3* (12) -2 (3- 2) +3k 2. Now 3k - 2 is even by inductive hypothesis. Therefore, 3k- 2 2m for some integer m. Hence, (3- 2) +3 -2 2m3 2 2(m+3k) which is even (because m+3k is an integer). It follows that 3k+1 -2 is even, which is what we needed to show