In each question below, some statements are given followed by two conclusions…
2025
In each question below, some statements are given followed by two conclusions numbered I and II. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements, disregarding commonly known facts. Give answer
Statements:
Only a few Trophy is good
All good is down
No down is hunger
Conclusions:
I. Some good is hunger
II. Some trophy being hunger is a possibility
- A.
If only conclusion I follows
- B.
If only conclusion II follows
- C.
If either conclusion I or II follows
- D.
If neither conclusion I nor II follows
- E.
If both conclusions I and II follow
Attempted by 7 students.
Show answer & explanation
Correct answer: B
Concept
In syllogism, a definite conclusion must hold in EVERY possible diagram allowed by the statements, while a "possibility" conclusion only needs at least ONE consistent diagram in which it is true. Two rules drive this set: (i) a universal chain "All A is B" together with "No B is C" forces "No A is C" (A and C are disjoint); (ii) "Only a few A is B" means some A is B AND some A is not B, and it leaves the not-B part of A free to relate to anything else unless another statement restricts it.
Application
From "All good is down" and "No down is hunger": Good is wholly inside Down, and Down is wholly outside Hunger. So Good is entirely outside Hunger — no Good can be Hunger.
Test "Some good is hunger": this asserts an overlap between Good and Hunger, but step 1 shows they are disjoint. So this statement is definitely FALSE — it does not follow.
"Only a few Trophy is good" gives some Trophy inside Good (those are inside Down, hence outside Hunger) and some Trophy outside Good, with no rule tying that outside part to Hunger.
Test "Some trophy being hunger is a possibility": since the non-good Trophies are unrestricted with respect to Hunger, we can draw a consistent diagram where a few of them lie in Hunger. A valid possibility diagram exists, so this possibility conclusion FOLLOWS.
Cross-check
Conclusion I claims a forced overlap that the disjointness rule forbids, so it can never hold. Conclusion II only claims a possibility, and one consistent diagram is enough to establish it. Hence exactly one of the two conclusions follows: the second one alone.