In the question below are given three statements followed by four conclusions…
2023
In the question below are given three statements followed by four conclusions numbered I, II, III and IV. You have to take the given 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 given statements, disregarding commonly known facts.
Statements: Some eyes are ears. Some ears are lungs. All lungs are hands.
I. Some hands are eyes.
II. Some hands are ears.
III. Some lungs are eyes.
IV. No hand is eye.
- A.
None follow
- B.
Only IV follows
- C.
Only II follows
- D.
Only III follows
Attempted by 1 students.
Show answer & explanation
Correct answer: C
Concept: In syllogisms, two statements combine into a valid conclusion only through their shared (middle) term. When a particular statement ("Some X are Y") and a universal statement ("All Y are Z") share a term Y that is the SUBJECT of the universal statement, every member of X that also falls under Y is, by the universal statement, guaranteed to fall under Z too — so a valid particular conclusion ("Some X are Z") follows. Two particular statements ("Some X are Y") sharing a middle term, by contrast, never distribute it, so no definite link between their other terms can be drawn — such a combination only shows a possibility, never a certainty.
Combine "Some ears are lungs" with "All lungs are hands": here the shared term "lungs" is the subject of the universal statement, so the ears that are lungs are necessarily hands as well. This gives "Some ears are hands", which converts to "Some hands are ears" — exactly Conclusion II.
Combine "Some eyes are ears" with "Some ears are lungs": both are particular statements sharing the middle term "ears". Two particular statements never yield a definite conclusion, because the portion of ears overlapping eyes need not be the same portion that overlaps lungs.
Because no definite link is established between eyes and lungs/hands, a shared member between hands and eyes, and between lungs and eyes, is only possible, not certain — so neither of those two conclusions is guaranteed in every valid diagram.
A conclusion that flatly denies any overlap between eyes and hands is also not guaranteed, since a valid diagram can be drawn where they DO share a member through the ears–lungs–hands chain — so a blanket denial cannot be treated as certain either.
Cross-check with a Venn diagram: draw ears as one circle with a sub-region overlapping eyes and a separate sub-region overlapping lungs (the two sub-regions may or may not coincide). Since lungs sits wholly inside hands, the lungs–ears overlap region is automatically inside hands too — this holds in every valid diagram, confirming Conclusion II. Sliding the eyes–ears overlap region in or out of the lungs sub-region shows the other three conclusions hold in some diagrams and fail in others, so none of them is certain.
Hence only Conclusion II follows.