Among the following propositions, two are related in such a way that one is…

Concept: In traditional (Aristotelian) categorical logic, every categorical statement about a subject S and predicate P takes one of four standard forms: A (universal affirmative — "All S are P"), E (universal negative — "No S are P"), I (particular affirmative — "Some S are P"), and O (particular negative — "Some S are not P"). The Square of Opposition defines how pairs of these forms, sharing the same S and P, relate to one another. Two statements are contradictories when exactly one of them must be true and the other must be false, in every possible case — that is precisely what it means for one to be "the denial of the other". The two contradictory pairs on the square are A↔O and E↔I.

Application:

1. (a) "All women are equal to men" is a universal affirmative statement about the same subject-predicate pair — the A form.

2. (b) "Some women are equal to men" is a particular affirmative statement — the I form.

3. (c) "Some women are not equal to men" is a particular negative statement — the O form.

4. (d) "No women are equal to men" is a universal negative statement — the E form.

5. (a) is the A form and (c) is the O form, and A and O are contradictories: if "All women are equal to men" is true, then "Some women are not equal to men" must be false, and if the universal is false, the particular-negative must be true — exactly one of the two always holds. So each is exactly the denial of the other, and (a), (c) is the required pair.

Cross-check (why the other codes fail):

• (a) and (b) — A and I — stand in subalternation, not contradiction: if the universal (a) is true, the particular (b) is automatically true too, so both can be true together; they don't satisfy "exactly one true, one false".

• (a) and (d) — A and E — are contraries: they cannot both be true, but they can both be false at once (e.g., when only some women, but not all and not none, are equal to men), so this pair also fails to be a strict denial relationship.

• (c) and (d) — O and E — also stand in subalternation: if the universal negative (d) is true, the particular negative (c) is automatically true too, so both can hold together rather than one denying the other.

Result: Only (a) and (c) are true contradictories — one is exactly the denial of the other. The correct code is "(a) and (c)".