In some cases, there are propositions that cannot both be true and both be false. Propositions that have this relationship are called contradictories.

Example: A and O:

If you accept the O proposition "Some bread is not nutritious," then you cannot also accept the A proposition, "All bread is nutritious," and vice versa. They cannot both be true.

O and A cannot both be false. The only way for A to be false is for there to be at least one S that is not P (some bread that is not nutritious), and in that case O is true. Similarly, the only way for O to be false is for there to be not even one S that is not P (not even some bread that is not nutritious), and in that case all S are P (all bread is nutritious) -- the A proposition is true.

Example: E and I:

E and I are also contradictories. They cannot both be true and they cannot both be false. If it is false that no bread is nutritious, that could only be because at least some bread is nutritious, in which case I is true. On the other hand, if I is false, that means not even one S is P, and thus it would be true to say that no S is P -- E would be true.