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Select the mistake that is made in the proof given below. Theorem. Fo.pdf

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Select the mistake that is made in the proof given below. Theorem. For any two integers, x and y, if 3 divides x and 3 divides y, then 3 also divides x+2y. Proof. Since 3 divides x,x=3k for some integer k. Since 3 divides y,y=3k for some integer k. Plugging in the expression 3k for x and 3k for y into x+2y gives x+2y=3k+2(3k)=3k+6k=9k=3(3k) Since k is an integer, 3k is also an integer. Since x+2y=3m, where m=3k is an integer, 3 divides x+2y. Failure to properly introduce variable. Generalizing from examples. Assuming facts that have not yet been proven. Misuse of existential instantiation..

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Select the mistake that is made in the proof given below. Theorem. For any two integers, x and y, if 3 divides x and 3 divides y, then 3 also divides x+2y. Proof. Since 3 divides x,x=3k for some integer k. Since 3 divides y,y=3k for some integer k. Plugging in the expression 3k for x and 3k for y into x+2y gives x+2y=3k+2(3k)=3k+6k=9k=3(3k) Since k is an integer, 3k is also an integer. Since x+2y=3m, where m=3k is an integer, 3 divides x+2y. Failure to properly introduce variable. Generalizing from examples. Assuming facts that have not yet been proven. Misuse of existential instantiation.

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