In the question given below two statements are given, which are followed by…
2022
In the question given below two statements are given, which are followed by two conclusions I and II. Assuming that the statements are true. Decide which conclusion logically follows the given statements. Statements: No scooter is ball. No ball is wicket. Conclusions: (I) No scooter is wicket. (II) All wickets are scooter.
- A.
Only conclusion I follows
- B.
Only conclusion II follows
- C.
Both conclusion I and II follow
- D.
Neither conclusion I nor conclusion II follows
Attempted by 65 students.
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Correct answer: D
Given: No scooter is ball. No ball is wicket.
Analysis:
Conclusion I (No scooter is wicket): Does not follow. The premises only state that scooters are disjoint from balls and balls are disjoint from wickets; they say nothing that forces scooters and wickets to be disjoint.
Conclusion II (All wickets are scooter): Does not follow. There is no information that makes wickets a subset of scooters.
Counterexample showing both conclusions can be false while premises remain true:
Let scooters = {s1}, balls = {b1}, wickets = {s1, w2}.
Then no scooter is a ball (s1 not in {b1}) and no ball is a wicket ({b1} not in {s1,w2}), so both premises hold.
But some scooter (s1) is a wicket, so Conclusion I is false; and wicket w2 is not a scooter, so Conclusion II is false.
Therefore, neither conclusion follows from the given statements. The correct choice is: Neither conclusion I nor conclusion II follows.