Let's look at the propositions, "Some S are P" (I) and "Some S are not P" (O). Propositions I and O cannot both be false. This relationship is called
Can I and O both be true? Yes--that happens quite often. For instance, some animals are mammals, some are not.
However, I and O can never both be false. Any given object in the
class of Ss must either be P or not be P. If it is P, that makes the I proposition true. If it is not P, that makes the O
proposition true. For instance, any given animal either is a mammal or is not.