Consider the following statement. For every integer m, 7m + 4 is not divisible by 7. Construct a proof for the statement by selecting senten

Question

Consider the following statement. For every integer m, 7m + 4 is not divisible by 7. Construct a proof for the statement by selecting sentences from the following scrambled list and putting them in the correct order. Suppose that there is an integer m such that 7m + 4 is divisible by 7.Subtracting 4m from both sides of the equation gives 7 = 4k − 4m = 4(k − m).By definition of divisibility 4m + 7 = 4k, for some integer k.By definition of divisibility 7m + 4 = 7k for some integer k.Dividing both sides of the equation by 7 results in 4 7 = k − m.Dividing both sides of the equation by 4 results in 7 4 = k − m.But k − m is an integer and 7 4 is not an integer.Suppose that there is an integer m such that 7m + 4 is not divisible by 7.But k − m is an integer and 4 7 is not an integer.Subtracting 7m from both sides of the equation gives 4 = 7k − 7m = 7(k − m).

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Ngọc Diệp 3 years 2021-09-03T03:39:41+00:00 1 Answers 8 views 0

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  1. Eirian
    0
    2021-09-03T03:41:05+00:00
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    Answer:

    A proof for the statement by selecting the given sentences are as follows;

    Suppose there is an integer m such that 7·m + 4 is divisible by 7

    By definition of divisibility, 7·m + 4 = 7·k for some integer k

    Subtracting 7·m from both sides of the equation gives 4 = 7·k – 7·m = 7·(k – m)

    Dividing both sides of the equation by 7 results in 4/7 = k – m

    But k – m is an integer and 4/7 is not an integer

    Therefore, for every integer m, 7·m + 4 is not divisible by 7

    Step-by-step explanation:

    The given equation can be expressed as follows;

    Where 7·m + 4 is divisible by 7, we have;

    7·m + 4 = 7·k

    Where ‘k’ is an integer

    We have;

    7·m + 4 – 7·m = 4 = 7·k – 7·m

    ∴ k – m = 4/7, where k – m is an integer

    ∴ k – m cannot be equal to 4/7, from which we have;

    7·m + 4 cannot be divisible by 7.

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