State the universal contraposition rule: contrapositive valid forms.

• A. Contraposition is valid for I and O propositions only; e.g., 'Some S are P' contrapositive: 'Some non-P are not non-S.'
• B. Contraposition is valid for E and O propositions only; e.g., 'No S are P' contrapositive: 'No non-P are non-S.'
• C. Contraposition is valid for A and E propositions; e.g., 'All S are P' contrapositive: 'All non-P are non-S.' Similarly, 'No S are P' contrapositive: 'No non-P are non-S.'
• D. Contraposition is valid for all four proposition forms.

Answer: (C)

The main idea here is that contraposition can be applied to universal categorical propositions and still preserve truth. When a universal statement links S and P, you can form a contrapositive by switching to the complements of the terms.

From All S are P, it follows that anything that is not P cannot be S. So the contrapositive is All non-P are non-S. Similarly, No S are P means S lies entirely outside P, and the contrapositive becomes No non-P are non-S (equivalently, All not-P are S). These two forms are the valid universal contraposition forms.

Existential, or particular, statements like Some S are P or Some S are not P do not have universally valid contrapositives, because the truth of the original does not guarantee the truth of a corresponding statement about all non-P or non-S.