6. proof by generalization from generic particular that the sum of an odd integer and an even integer is odd. (3 marks)

Step-by-step explanation:

Consider the variables a and b, whereas a is an odd integer and b is an even integer.

By definition: a = 2x + 1 and b = 2y    (values for which x;y are integers)

The summation of a and be would be: a + b = 2x + 2y + 1

Simplifying the equation: 2x + 2y + 1

                                        =2(x + y) + 1        

                                        =2m + 1           (values for which m = x + y is an integer)

Therefore by definition of an odd integer (2x + 1), it is clear  that the sum of an odd integer and an even integer is odd.

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