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. By definition of divisibility 7m + 4 = 7k for some integer k. Subtracting 7m from both sides of the equation gives 4 = 7k – 7m = 7(k – m). Dividing both sides of the equation by 7 results in - = k - m. 7 Subtracting 4m from both sides of the equation gives 7 = 4k – 4m = 4(k – m). 7 But k – m is an integer and - is not an integer. Suppose that there is an integer m such that 7m + 4 is divisible by 7. 7 = k - m. 4 Dividing both sides of the equation by 4 results in - But k – m is an integer and - is not an integer. By definition of divisibility 4m + 7 = 4k, for some integer k. Suppose that there is an integer m such that 7m + 4 is not divisible by 7. Proof by contradiction: 1. ---Select-- 2. ---Select--- 3. ---Select-- 4. ---Select-- 5. ---Select-- 6. This result is a contradiction. Hence we can conclude that the supposition is false and the given statement is true.

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. By definition of divisibility 7m + 4 = 7k for some integer k. Subtracting 7m from both sides of the equation gives 4 = 7k – 7m = 7(k – m). Dividing both sides of the equation by 7 results in - = k - m. 7 Subtracting 4m from both sides of the equation gives 7 = 4k – 4m = 4(k – m). 7 But k – m is an integer and - is not an integer. Suppose that there is an integer m such that 7m + 4 is divisible by 7. 7 = k - m. 4 Dividing both sides of the equation by 4 results in - But k – m is an integer and - is not an integer. By definition of divisibility 4m + 7 = 4k, for some integer k. Suppose that there is an integer m such that 7m + 4 is not divisible by 7. Proof by contradiction: 1. ---Select-- 2. ---Select--- 3. ---Select-- 4. ---Select-- 5. ---Select-- 6. This result is a contradiction. Hence we can conclude that the supposition is false and the given statement is true.

Name: Consider the following statement.For every integer m, 7m + 4 is not d
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Description: 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.By definition of divisibility 7m +

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.2: Mathematical Induction

Problem 50E: Show that if the statement 1+2+3+...+n=n(n+1)2+2 is assumed to be true for n=k, the same equation...

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