Equivalent Immediate Inferences of the four Categorical Statements:
All S is P
= No S is non-P (obverse)
= All non-P is non-S (contrapositive)
No S is P
= All S is non-P (obverse)
= No P is S (converse)
Some S is P
= Some S is not non-P (obverse)
= Some P is S (converse)
Some S is not P
= Some S is non-P (obverse)
= Some non-P is not non-S (contrapositive)
Immediate inferences work in reverse:
All S is non-P
= No S is P (obverse)
All non-S is non-P
= All P is S (contrapositive)
No S is non-P
= All S is P (obverse)
Some S is non-P
= Some S is not P (obverse)
Some S is not non-P
= Some S is P (obverse)
Some non-S is not non-P
= Some P is not S (contrapositive)
Immediate inferences can be combined:
No non-S is P
= No P is non-S = All P is S (converse, obverse)
Some non-S is P
= Some P is non-S = Some P is not S (converse, obverse)
Other translations:
All non-S is P
= All non-P is S (contrapositive)
No non-S is non-P
= All non-S is P (obverse)
Some non-S is not P
= Some non-P is not S (contrapositive)
Some non-S is non-P
= Some non-S is not P (obverse)
All of this and more is included in this complete Immediate Inference Chart.