The difference of any two odd integers is even. Proof: Let m and n be any odd integers. By definition of odd, there are integers r and s so that m can be expressed in terms of r and n can be expressed in terms of s as follows. m = n = Write m - n in terms ofr and s and factor out a 2 to obtain m - n = is an integer because differences of integers are integers. Now Therefore, m - n = 2· (an integer), and so m - n is even by definition of even

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.