Integer Parities

Number Theory Level 1

If ${\color{#3D99F6}{a}},$ ${\color{#20A900}{b}},$ and ${\color{#D61F06}{c}}$ are integers, is it possible that ${\color{#3D99F6}{a}}+{\color{#20A900}{b}},$ ${\color{#3D99F6}{a}}+{\color{#D61F06}{c}},$ and ${\color{#20A900}{b}}+{\color{#D61F06}{c}}$ are all odd numbers?

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