Theorem. The product of an even integer and any other integer is even. Proof. Let x be an even integer and y be an arbitrary integer. Since x is even, x=2k for some integer k. Therefore, xy=2m for some integer m, which means that xy is even. Question 1 options: Misuse of existential instantiation. Generalizing from examples. Assuming facts that have not yet been proven. Failure to properly introduce a variable