An immediate inference draws a conclusion from a single proposition, with no second premise. Before we can make the three classic ones, we need one more idea about classes. In a Venn diagram, everything outside a circle forms a class too.
Key idea
The complement of a class is everything that is not in it, written with "non-": the complement of winners is non-winners. The complement of non-winners is winners again.
Why it works
A class and its complement split the whole world in two with nothing left over and nothing counted twice: each thing is either a winner or not. Opposite words do not do that. "Losers" leaves out everyone who never played, and some people are neither. Because a complement leaves no gap, swapping a statement about P for one about non-P can keep the meaning exactly, which is what obversion and contraposition will do.
Worked example
Worked example: Complement or opposite?
Is "children" the complement of "adults"?
- The complement of adults is everything that is not an adult: non-adults.
- Teenagers are neither adults nor (in everyday speech) children, and a table is neither. So "children" leaves things out.
Answer: no: the complement is non-adults
Worked example: Two complements
What is the complement of "non-members"?
- The complement is everything outside the class of non-members.
- Everything that is not a non-member is a member.
Answer: members
In a two-circle Venn diagram, the class non-P is everything outside the P circle: region 1 (S only) and region 4 (outside both). That is why statements about non-P can be drawn on the same picture as statements about P.
Common mistake
Using the opposite word instead of the complement: the complement of "winners" is "non-winners", not "losers", since some may not have played. Check: is there anything that is neither? If so, the opposite word is not the complement.