Consider the following solution that proves that the sum of…
Consider the following solution that proves that the sum of two odd integers is not odd.Assume there exist two odd integers a and b such that a+b is odd.Let a an odd number and therefore can be written as: a = 2k + 1 (for some k integer)Let b an odd number and therefore can be written as: b = 2m+1 (for some m integer)Now consider the sum a+b: a + b = 2k+1 + 2m+1 = 2(k+m+1) which is the definition of an even integer which contradicts the assumption that a+b is odd.Which of the following proof strategies was followed above?
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Consider the following solution that proves that for any integers a and b, the difference a−b is even or odd.Case 1: a and b have the same parity (both even or both odd). Then a−b is even.Case 2: a and b have different parity (one even, one odd). Then a−b is odd.All possibilities are covered, so the statement holds.Which of the following proof strategies was followed above?
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