5. (10 points) Fill in the blanks in the following proof by contraposition that for all...

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5. (10 points) Fill in the blanks in the following proof by contraposition that for all integers n, if 5 Xn, then 5 Xn. Proof (by contraposition): [The contrapositive is : For all integers n, if 5|n, then 5|n.] Suppose n is any integer such that ___(A)___. [We must show that __(B)___.] By definition of divisibility, n = ____(C)____ for some integer k. By substitution, n ___(D)___= 5(5k). But 5k is an integer because it is a product of integers. Hence n = 5 (an integer), and so, ____(E)____ [as was to be shown]. = 5. (10 points) Fill in the blanks in the following proof by contraposition that for all integers n, if 5 Xn, then 5 Xn. Proof (by contraposition): [The contrapositive is : For all integers n, if 5|n, then 5|n.] Suppose n is any integer such that ___(A)___. [We must show that __(B)___.] By definition of divisibility, n = ____(C)____ for some integer k. By substitution, n ___(D)___= 5(5k). But 5k is an integer because it is a product of integers. Hence n = 5 (an integer), and so, ____(E)____ [as was to be shown]. =

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