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.