Which of the following propositions are such that the truth of one entails the…
2026
Which of the following propositions are such that the truth of one entails the falsity of the other but not vice versa?
A. All bananas are fruits.
B. No bananas are fruits.
C. Some bananas are fruits.
D. Some bananas are not fruits.
Choose the correct answer from the options given below:
- A.
A and D Only
- B.
C and D Only
- C.
A and B Only
- D.
C and D Only
Attempted by 14 students.
Show answer & explanation
Correct answer: C
The question requires identifying a pair of propositions where the truth of one entails the falsity of the other, but not vice versa.
Propositions A (All bananas are fruits) and B (No bananas are fruits) are Contraries. If A is true, B must be false because a subject cannot be entirely included and entirely excluded from a class simultaneously.
However, if A is false (not all bananas are fruits), B does not necessarily become true (some might still be fruits). This asymmetric relationship matches the condition given.
In contrast, Contradictories (like A and D) have a symmetric relationship where the falsity of one guarantees the truth of the other.
Thus, the pair A and B is the correct answer.