Which of the following statements are true regarding sub-contrary…
2024
Which of the following statements are true regarding sub-contrary propositions?
A. If one is true, the other must be false
B. They cannot both be false
C. If one is false, the other must be true
D. They can both be true
Choose the correct answer from the options given below:
Answer: B. B, C and D Only — ConceptIn the traditional square of opposition, the sub-contrary relation holds between the particular affirmative I-proposition, Some S is P, and the…
- A.
A and C Only
- B.
B, C and D Only
- C.
A, B and C Only
- D.
A and D Only
Show answer & explanation
Correct answer: B
Concept
In the traditional square of opposition, the sub-contrary relation holds between the particular affirmative I-proposition, Some S is P, and the particular negative O-proposition, Some S is not P. Two sub-contraries can never be false together: at least one of them must be true. They may, however, be true together, so their truth values are not mutually exclusive.
Application
Each statement in the list is now measured against that definition.
Statement | What it claims | Status under the sub-contrary relation |
|---|---|---|
A | The truth of one member forces the falsity of the other | Does not hold, because sub-contraries may be true together |
B | The two members cannot both be false | Holds; this is the defining property of the relation |
C | The falsity of one member forces the truth of the other | Holds; it is the same law of the relation restated |
D | The two members can both be true | Holds; joint truth is permitted by the relation |
A concrete model settles the first and the last of these claims. In a class that contains both athletes and non-athletes, the I-proposition Some students are athletes and the O-proposition Some students are not athletes are true at the same time. Joint truth is therefore possible for a sub-contrary pair, which makes the claim of mutual exclusivity of truth false and the claim of possible joint truth true.
The remaining two claims follow from the traditional assumption that the subject class is not empty. Suppose Some S is P is false. Then no S is P, and therefore Some S is not P must be true. The same reasoning runs in the opposite direction. So the falsity of either member guarantees the truth of the other, and the pair can never be false together.
Cross-check
Placing the relation beside its neighbours on the square confirms the pattern:
Relation | Both true possible? | Both false possible? |
|---|---|---|
Contraries, universal affirmative and universal negative | No | Yes |
Sub-contraries, particular affirmative and particular negative | Yes | No |
Contradictories, universal affirmative with particular negative | No | No |
Sub-contraries are the row that permits joint truth while forbidding joint falsity. The statements that match that pattern are B, C and D, so the true set is B, C and D.