In each of the following questions two statements are given and these…
2024202420232024
In each of the following questions two statements are given and these statements are followed by two conclusions numbered (1) and (2). You have to take the given two statements to be true even if they seem to be at variance from commonly known facts. Read the conclusions and then decide which of the given conclusions logically follows from the two given statements, disregarding commonly known facts. Statements: Some cows are crows. Some crows are elephants. Conclusions: Some cows are elephants. All crows are elephants.
- A.
Only (1) conclusion follows
- B.
Only (2) conclusion follows
- C.
Either (1) or (2) follows
- D.
Neither (1) nor (2) follows
Attempted by 61 students.
Show answer & explanation
Correct answer: D
Answer: Neither (1) nor (2) follows.
Reasoning:
Why "Some cows are elephants" does not follow: The premises only state that some cows are crows and some crows are elephants. The specific cows that are crows might be different from the specific crows that are elephants, so there is no guaranteed overlap between cows and elephants.
Why "All crows are elephants" does not follow: The second premise says only that some crows are elephants, which does not imply that every crow is an elephant.
Concrete counterexample: Let Crows = {c1, c2}, Cows = {c1}, Elephants = {c2}. Then "Some cows are crows" (c1) and "Some crows are elephants" (c2) are both true, but no cow is an elephant and not all crows are elephants.
Conclusion: Because both conclusions can fail under the premises, neither conclusion (the claim that some cows are elephants, nor the claim that all crows are elephants) follows logically.