1. X X X X Logical relations among categorical propositions S P S P S P
Each universal proposition, represented in the top row, is mutually contradictory with exactly one particular proposition,
represented directly below it. No other logical relations hold among any other propositions.
Contrapositive
Universal affirmative Universal negative Converse universal affirmative universal negative
All S are P No S are P All P are S All non-S are P
= (x)(Sx  Px) = (x)(Sx  Px) = (x)(Px  Sx) = (x)(Sx  Px)
S P
S P
S P
S P
mutually
contradictory
mutually
contradictory
mutually
contradictory
mutually
contradictory X
S P
S P
S P
S P X X X
Contrapositive
Particular negative Particular affirmative Converse particular negative particular affirmative
Some S are not P Some S are P Some P are not S Some non-S are non-P
= (x)(Sx  Px) = (x)(Sx  Px) = (x)(Px  Sx) = (x)(Sx  Px)