Read the following statement carefully and identify the conclusion that follows. Statement: All kids are students. Some students are athletes. No athlete is a scholar. Conclusions: I. Some kids may be athletes. II. No kid is a scholar.
- (a)Only I follows
- (b)Only II follows
- (c)Both I and II follow
- (d)Neither I nor II follows
Answer
Why
Correct — A.
Rule: a 'may be' conclusion follows if the statements allow it; a definite one follows only if they force it.
I: kids sit inside students, and some students are athletes. Nothing keeps kids out of that group, so 'Some kids may be athletes' follows.
II: the statements bar only athletes from being scholars. A kid who is not an athlete can still be a scholar, so 'No kid is a scholar' is not forced.
Only I follows → option (a).
Why the others are wrong
- (b)Only II follows — Only II gets both wrong. II is not forced, since a kid who is not an athlete could be a scholar, and I holds as a possibility.
- (c)Both I and II follow — Both would need 'No kid is a scholar' to be certain. It is not: a kid who is not an athlete can be a scholar without breaking any statement.
- (d)Neither I nor II follows — Neither misses that I is a possibility claim. No statement separates kids from athletes, so 'may be' holds.
Concept
A definite conclusion must hold in every diagram the statements allow. A possibility conclusion ('may be') needs just one allowed diagram in which it is true.
Here kids sit inside students. Athletes overlap students and stay apart from scholars. Kids can be drawn touching athletes, so I follows. Kids can also be drawn touching scholars, so II fails.
Conclusion II fails the moment one allowed diagram breaks it. A kid who is a scholar and not an athlete breaks no statement, so II cannot be forced.
Key facts
- A possibility conclusion follows if at least one diagram allowed by the statements makes it true.
- A definite conclusion follows only if every allowed diagram makes it true.
- 'No athlete is a scholar' says nothing about students or kids who are not athletes.
Study next
Common traps
- Carrying 'No athlete is a scholar' over to kids, as if every kid were an athlete.
- Rejecting 'Some kids may be athletes' because no statement links kids to athletes, when a possibility needs no link.
12 Sep 2024, 12:30, Reasoning Q.9 sets the same trap: all cards are postcards, some postcards are books, and 'No card is a book' does not follow. It keys Only conclusion I.
12 Sep 2024, 09:00, Reasoning Q.11 keys a possibility conclusion alone: 'All diaries being notebooks is a possibility'.
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