Let $a$ be a positive even integer and $b$ be a negative odd integer. Consider $a - b$:

Since $b$ is negative, subtracting $b$ is the same as adding $|b|$:

$a - b = a + |b|$

The sum of a positive even number and a positive odd number is always positive and odd.

For example, $a = 2$ and $b = -3$: $a - b = 2 - (-3) = 5$ (positive and odd).