Consider the following statement. For every integer m, 7m + 4 is not divisible by 7. Some of the sentences in the following scrambled list can be used to prove the statement by contradiction. But k m is an integer and 74 is not an integer. But k m is an integer and 47 is not an integer. Subtracting 7m from both sides of the equation gives 4 = 7k 7m = 7(k m). Suppose that there is an integer m such that 7m + 4 is not divisible by 7. By definition of divisibility 7m + 4 = 7k for some integer k. Dividing both sides of the equation by 7 results in 47 = k m. By definition of divisibility 4m + 7 = 4k, for some integer k. Dividing both sides of the equation by 4 results in 74 = k m. 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)