Which of the following statements are subalternate as per traditional square…

Concept

The traditional square of opposition arranges the four standard categorical propositions: the A-form, a universal affirmative ("All S are P"); the E-form, a universal negative ("No S are P"); the I-form, a particular affirmative ("Some S are P"); and the O-form, a particular negative ("Some S are not P"). Subalternation is the relation that holds between a universal proposition and the particular proposition of the same quality — that is, between A and I, and between E and O. The universal member is called the superaltern and the particular member the subaltern, and the relation is one-directional in each direction of truth value: if the universal is true the particular must be true (truth descends), and if the particular is false the universal must be false (falsity ascends).

Applying the rule to these statements

Classify each given statement by quantity (universal or particular) and by quality (affirmative or negative):

• Statement A, "All plants are green organisms", affirms the predicate of the entire subject class, so it is universal and affirmative — the A-form.

• Statement B, "No plants are green organisms", denies the predicate of the entire subject class, so it is universal and negative — the E-form.

• Statement C, "Some plants are not green organisms", denies the predicate of at least one member, so it is particular and negative — the O-form.

• Statement D, "Some plants are green organisms", affirms the predicate of at least one member, so it is particular and affirmative — the I-form.

Now pair each universal with the particular that shares its quality. The A-form pairs with the I-form, which is statement A with statement D. The E-form pairs with the O-form, which is statement B with statement C. Both are genuine subalternation pairs, but only one of them appears among the answers offered here: the B and C pairing is not on offer, so the subalternate pair available to select is A and D.

Cross-check: the other relations of the square

Every other combination of these four statements falls under a different relation of the square, which confirms that no other pairing offered here is a subalternation:

Therefore the subalternate pair among the answers given is A and D only.