Immediate inference immediate inference proposition . For instance, from the statement "All toads are green." we can make the immediate inference that "No toads are not green." There are a number of immediate inferences which can validly be made using logical operations , the result of which is a logically equivalent statement form to the given statement. There are also invalid immediate inferences which are syllogistic fallacies .Valid immediate inferencesConverse Given a type E statement, from the traditional square of opposition , "No S are P .", one can make the immediate inference that "No P are S " which is the converse of the given statement. Given a type I statement, "Some S are P .", one can make the immediate inference that "Some P are S " which is the converse of the given statement.Obverse Given a type A statement, "All S are P .", one can make the immediate inference that "No S are non-P " which is the obverse of the given statement. Given a type E statement, "No S are P .", one can make the immediate inference that "All S are non-P " which is the obverse of the given statement. Given a type I statement, "Some S are P .", one can make the immediate inference that "Some S are not non-P " which is the obverse of the given statement. Given a type O statement, "Some S are not P .", one can make the immediate inference that "Some S are non-P " which is the obverse of the given statement.Contrapositive Given a type A statement, "All S are P .", one can make the immediate inference that "All non-P are non-S " which is the contrapositive of the given statement. Given a type O statement, "Some S are not P .", one can make the immediate inference that "Some non-P are not non-S " which is the contrapositive of the given statement.Invalid immediate inferences Cases of the incorrect application of the contrary, subcontrary and subalternation relations are syllogistic fallacies called illicit contraryillicit subcontrary , and illicit subalternation . Cases of incorrect application of the contradictory relation are so infrequent, that an "illicit contradictory" fallacy is usually not recognized.Illicit contrary It is false that all A are B , therefore no A are B . It is false that no A are B , therefore all A are B .Illicit subcontrary Some A are B , therefore it is false that some A are not B . Some A are not B , therefore some A are B .Illicit subalternation (Superalternation) Some A are not B , therefore no A are B . It is false that all A are B , therefore it is false that some A are B .
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