X X X X Logical relations among categorical propositions S P S P S P

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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)