A and E statements (contraries) can both be false, but both cannot be true.

 

A and O statements, and E and I statements are always the contradiction of one another, so if A is true O is false. If O is true then A is false. If E is true then I is false. If I is true then E is false.

 

A and I statements, and E and O statements have a relationship too. If A is true then I is true. If E is true then O is true. If A is false we can't be sure about I. If E is false we can't be sure about O. If I is true or false we can't be sure about A. If O is true or false we can't be sure about E.

 

I and O statements have a relationship too. If I is false then O must be true. If O is false then I must be true. If I is true O can be either true or false. If O is true then I can be either true or false. These are sub contraries.

 

Play with this square until the obvious nature of these relationships becomes second nature. This can be a wonderful tool for clear thinking. It works.

 

What about using statements in arguments?