Logic 4.5

Traditional Square of Opposition:

Contradictory: Complete opposition between propositions. One of the contradictory set must be true and the other must be false.
Contrary: Expresses only partial opposition; at least one must be false, however, both might be false.
Subcontrary: Expresses only partial opposition; at least one must be true, however, both might be true.
Subalternation: Truth transmits only downward; falsity transmits only upward.

Inferences that do not transmit their truth-values are said to be illicit.
Illicit Contrary:
It is false that all A are B
Therefore, no A are B
It is false that no A are B.
Therefore, all A are B.

Illicit Subcotrary:
Some A are B.
Therefore, it is false that some A are not B
Some A are not B.
Therefore, some A are not B.

Illicit Subalternation:
Some A are not B.
Therefore, no A are B.
It is false that all A are B.
Therefore, it is false that some A are B.

Remember the Existential Fallacy and distinguish between unconditionally valid inferences and conditionally valid inferences.