Two propositions are contradictory if A. They cannot both be true B. Of the…
2024
Two propositions are contradictory if
A. They cannot both be true
B. Of the pair, exactly one is true and exactly one is false
C. They can both be false
D. They cannot both be false
Choose the correct answer from the options given below:
Answer: D. A, B and D only — ConceptContradictory propositions are a pair whose truth values must always be opposite: one is true and the other is false. Equivalently, they cannot both be…
- A.
A and C only
- B.
A, B and C only
- C.
B only
- D.
A, B and D only
Show answer & explanation
Correct answer: D
Concept
Contradictory propositions are a pair whose truth values must always be opposite: one is true and the other is false.
Equivalently, they cannot both be true, exactly one is true and one is false, and they cannot both be false.
Application
The statement “They cannot both be true” follows from opposite truth values, so it is a necessary property of contradictory propositions.
The statement “Exactly one is true and exactly one is false” states the full defining condition for contradiction.
The statement “They can both be false” conflicts with contradiction because contradictory propositions cannot share the same truth value.
The statement “They cannot both be false” also follows from opposite truth values, so it is a necessary property of contradictory propositions.
Contrast
Contraries cannot both be true, but they may both be false.
Subcontraries cannot both be false, but they may both be true.
Contradictories have opposite truth values in every case.
Cross-check
Using the two possible cases, (true, false) and (false, true), exactly one member is true in each case; neither (true, true) nor (false, false) is allowed.
Therefore A, B and D hold, whereas C does not; the answer value is “A, B and D only”.