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If a,{\color{#3D99F6}{a}},a, b,{\color{#20A900}{b}},b, and c{\color{#D61F06}{c}}c are integers, is it possible that a+b,{\color{#3D99F6}{a}}+{\color{#20A900}{b}},a+b, a+c,{\color{#3D99F6}{a}}+{\color{#D61F06}{c}},a+c, and b+c{\color{#20A900}{b}}+{\color{#D61F06}{c}}b+c are all odd numbers?
Note: It is possible for all three sums to be even!
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