11.
Consider the following statements.
I. Some fairies are pixies
II. All pixies are magicians
III. No magicians are trolls
Based on the above statements, which of the following is correct:
a. Some trolls are pixies
b. Some fairies are magicians
c. All magicians are pixies
d. All pixies are fairies
Some fairies are pixies, all pixies are magicians, and no magicians are trolls form a classic syllogism testing logical deductions. The correct option follows directly from combining these statements using Venn diagram rules or distribution method.
Syllogism Statements Breakdown
Statements translate to: I (Some F are P), II (All P are M), III (No M are T). Pixies (P) link fairies (F) to magicians (M), while magicians exclude trolls (T). Combining I and II yields “Some F are M” definitively, as the “some” fairies overlap with all-inclusive pixies becoming magicians. No direct F-T or other relations exist beyond exclusions.
Option-by-Option Analysis
| Option | Statement | Valid? | Reason |
|---|---|---|---|
| a | Some trolls are pixies | No | Pixies are all magicians (II), but no magicians are trolls (III), so no pixies are trolls. Reverse (some T are P) fails. |
| b | Some fairies are magicians | Yes | Some F are P (I) + All P are M (II) = Some F are M. Definite conclusion via “some + all” rule. |
| c | All magicians are pixies | No | All P are M allows magicians outside pixies; no reverse inclusion given. |
| d | All pixies are fairies | No | Some F are P allows pixies outside fairies; no universal inclusion. |
Why This Matters for CSIR NET
Syllogisms test undistributed middles and complementary conclusions in exams like CSIR NET Life Sciences reasoning sections. Practice Venn diagrams: shade exclusions (no M-T), fill inclusions (P inside M), and check overlaps (F-P-M chain). Avoid assumptions beyond statements.
