resulting propositions from obversion are logically equivalent to the original statements in terms of truth-value, they are not semantically equivalent to their original statements in their standard form. Proof that the truth-value of the original statement is preserved by an obversion operation Consider all possible relationships between the Subject (S) and the Predicate (P) represented using sets: Case 1: S = P (S and P perfectly overlap) Case 2: S is a subset of P Case 3: P is a subset of S Case 4: S and P are two overlapping sets Case 5: S and P are disjoint sets Case 6: S is the universe with P being a subset of S Case 7: P is the universe with S being a subset of P Validity of statements after Obversion: The obversion operation is performed by changing the quality of the statement and replacing the predicate with its complement. 1. Statement: All S are P (Applicable for Case 1, 2, and 7) Obverse: No S are non-P Validity: YES 2. Statement: No S are P (Applicable for Case 5) Obverse: All S are non-P Validity: YES 3. Statement: Some S are P (Applicable for Case 1, 2, 3, 4, 6 and 7) Obverse: Some S are not non-P Validity: YES 4. Statement: Some S are not P (Applicable for Case 3, 4, 5 and 6) Obverse: Some S are non-P Validity: YES See also Aristotle Categorical proposition#Obversion Contraposition Conversion (logic) Inference Syllogism Term logic Transposition (logic) Footnotes Bibliography Brody, Bobuch A. "Glossary of Logical Terms". Encyclopedia of Philosophy. Vol. 5–6. Macmillan, 1973. Copi, Irving. Introduction to Logic. MacMillan, 1953. Copi, Irving. Symbolic Logic. MacMillan, 1979, fifth edition. Stebbing, Susan. A Modern Introduction to Logic. Cromwell Company, 1931. Immediate inference