Integer Parities

Number Theory Level 1

If ${\color{blue}{a}},$ ${\color{green}{b}},$ and ${\color{red}{c}}$ are integers, is it possible that ${\color{blue}{a}}+{\color{green}{b}},$ ${\color{blue}{a}}+{\color{red}{c}},$ and ${\color{green}{b}}+{\color{red}{c}}$ are all odd numbers?

Note: It is possible for all three sums to be even!