For which of the following forms of categorial propositions contraposition is valid?

A. Some S is P

B. Some S is not P

C. No S is P

D. All S is P

Choose the correct answer from the options given below:

Hence, among the above statements, statement B, C and D of categorial propositions contraposition is valid.

Hence, the correct answer is B, C and D only.

Additional Information

• A  categorical proposition is a simple proposition containing two terms, subject(S) and predicate (P), in which the predicate is either asserted or denied of the subject.
• Every categorical proposition can be reduced to one of four logical forms, named A, E, I and O.
• The 'A' proposition, is the universal affirmative usually translated as 'All S is P'.
• In the 'E' proposition, is the universal negative is usually 'No S is P'.
• The 'I' proposition, is the particular affirmative usually translated as 'Some S are P'.
• In the 'O' proposition, is the particular negative is usually translated as 'Some S are not P'

Key Points

• Contraposition is the inference in which the subject is interchanged with the complement of the predicate and the predicate is interchanged with the complement of the subject.
• In modern logic it is only valid for the A and O propositions. The valid contrapositive is logically equivalent to the original proposition.
• In traditional logic, the E proposition has a contrapositive by limitation which is the subaltern of the invalid E-contrapositive; i.e., the corresponding O proposition. The contrapositive by limitation is implied by the original but is not (usually) equivalent to it.