Two statements that cannot both be false, but can both be true, are called subcontrary.
For example, the statements
some apples are red
some apples are not red
cannot both be false, but they can both be true.
Personally, though, the main reason for cherishing the word subcontrary is just that it sounds so delightfully cross-grained and stubborn.
Word To Use Today: subcontrary. Sub- is Latin, and can mean almost anything, but most commonly it means under. The contrary bit of the word is also basically Latin: the word contrārius means opposite, and contrā means against.