The sum of any two odd integers is odd.

The statement that the sum of any two odd integers is odd is false. When we add two odd integers, we are essentially adding an odd number of odd units or quantities together. However, this can result in an even number. For example, adding 3 and 5 (both odd) gives us 8, which is an even number. Therefore, there are cases where the sum of two odd integers can be an even integer, making the statement false.