If the proposition ‘No reptiles are squirrels’ is given as false, then which…
2025
If the proposition ‘No reptiles are squirrels’ is given as false, then which of the following propositions can be inferred to be true?
A. Some reptiles are squirrels
B. All reptiles are squirrels
C. Some non-squirrels are not non-reptiles
D. Some reptiles are not squirrels
choose the most appropriate answer from the options given below:
- A.
A and B Only
- B.
B Only
- C.
C and D Only
- D.
A, C and D Only
Attempted by 6 students.
Show answer & explanation
Correct answer: D
The proposition 'No reptiles are squirrels' is an E-type (universal negative) statement. If this statement is false, its contradictory must be true according to the Square of Opposition.
The contradictory of 'No S are P' is 'Some S are P'.
Therefore, 'Some reptiles are squirrels' (Option A) must be true.
Since some reptiles are indeed squirrels, it logically follows that 'Some reptiles are not squirrels' (Option D) is also a valid inference in this context, as the existence of some reptiles being squirrels does not negate that others might not be.
Additionally, Option C ('Some non-squirrels are not non-reptiles') is logically equivalent to 'Some reptiles are squirrels' through obversion and conversion, making it true as well.
Option B ('All reptiles are squirrels') is not necessarily true because the falsity of 'No' only implies 'Some', not 'All'. Thus, A, C, and D are the correct inferences.