Syllogism: Possibility, Either-Or and "Only a Few"
Syllogism: Possibility, Either-Or and "Only a Few"
Newer syllogism questions test what may be true, not just what must be true. A possibility conclusion is valid if at least one diagram allows it without breaking any statement. Either-or pairs cover two cases of which one must hold. "Only a few A are B" says two things at once: some A are B, and some A are not.
1. Rules Box
| Conclusion type | Valid when |
|---|---|
| "X being Y is a possibility" | Some diagram satisfies all statements and the conclusion |
| Either I or II | Neither is certain, they involve the same two terms, and together they cover every case |
| Only a few A are B | Some A are B and some A are not B, both definite |
| Complementary pairs (for either-or) |
|---|
| Some A are B / No A is B |
| All A are B / Some A are not B |
A definite "No A is C" or "Some A are not C" kills the possibility "All A are C"
If one conclusion of a pair is already definite, do not mark either-or
✗ Some A are C is not definite, so it is not even possible | ✓ Not definite does not mean impossible; check the possibility separately
✗ Only a few teachers are writers means no teacher is a writer | ✓ It means some are and some are not
हिंदी नोट: संभावना वाले निष्कर्ष तभी सही हैं जब कोई ऐसा वेन आरेख बने जो सभी कथनों और निष्कर्ष को सत्य रखे। "कुछ/कोई नहीं" और "सभी/कुछ नहीं" युग्म पर "या तो I या II" लगता है। "केवल कुछ" का अर्थ है कुछ हैं और कुछ नहीं हैं।
Exam Pointer: Verified NTPC pattern: "only a few" statements (December 2020 CBT-1). Possibility, either-or and no-conclusion cases had no verified NTPC shift in our check and are tagged syllabus-based.
Pariksha Pattern: Every Way NTPC Asks This Topic
Pattern 1: Possibility conclusions
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. Statements: All cups are plates. Some plates are bowls. Conclusions: I. Some cups being bowls is a possibility. II. All bowls being cups is a possibility. Which follow?
Draw bowls overlapping the cups inside plates: I is possible. Drawing all bowls inside cups also keeps both statements true (those bowls are plates), so II is possible.
Answer: Both I and II
EXAMATLAS LEVEL
Q. Statements: No A is B. All B are C. Conclusions: I. All C being A is a possibility. II. Some A being C is a possibility. III. All A being C is a possibility. Which follow?
B lies inside C and outside A, so some C (the B part) are never A: I is impossible. A can overlap C outside B, so II is possible, and A can lie entirely inside C outside B, so III is possible too.
Answer: II and III
Pattern 2: Either-or pairs
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. Statements: Some boys are tall. All tall people are strong. Conclusions: I. All boys are strong. II. Some boys are not strong. Which follow?
Some boys are strong is certain, but whether all are is unknown. I and II are an All / Some-not pair on the same terms, so one must be true.
Answer: Either I or II
EXAMATLAS LEVEL
Q. Statements: Some A are B. No B is C. Conclusions: I. Some A are C. II. No A is C. III. Some A are not C. Which follow?
Some + No gives Some A are not C (III), which is definite. Between A and C nothing else is certain; I and II are a Some / No pair on the same terms, so one of them must hold.
Answer: III, and either I or II
Pattern 3: "Only a few"
[PYQ: NTPC CBT-1 28-Dec-2020 Shift-2]
EXAM LEVEL
Q. Statement: Only a few teachers are writers. Conclusions: I. Some teachers are not writers. II. All teachers are writers. Which follow?
"Only a few" means some teachers are writers and some are not. I follows; II contradicts it.
Answer: Only I
EXAMATLAS LEVEL
Q. Statements: Only a few birds are parrots. All parrots are green. Conclusions: I. Some birds are green. II. Some birds are not parrots. III. All birds being green is a possibility. IV. All birds are parrots. Which follow?
Some birds are parrots and parrots are green, so I follows. "Only a few" gives II directly. The non-parrot birds may also be green, so III is possible. IV contradicts "only a few".
Answer: I, II and III
Pattern 4: No definite conclusion and the either-or trap
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. Statements: All A are B. Some B are C. Conclusions: I. Some A are C. II. Some C are B. Which follow?
All + Some gives nothing definite between A and C, so I fails. Some B are C converts to Some C are B (II).
Answer: Only II
EXAMATLAS LEVEL
Q. Statements: Some X are Y. Some Y are Z. Conclusions: I. Some X are Z. II. No X is Z. III. All Z are X. Which follow?
Some + Some gives no definite link, so none of I, II or III is certain. But I and II are a Some / No pair on the same terms, and one of them must be true in every diagram.
Answer: Either I or II
60-Second Revision
- Possibility: find one diagram where everything holds.
- Either-or: neither definite, same two terms, complementary pair.
- Only a few A are B = some A are B + some A are not B.
- A definite negative rules out the matching "All" possibility.
Next Step: Syllogism done. Practise the syllogism set in the ExamAtlas RRB NTPC 2026 mock tests; sketch one quick Venn for each conclusion before marking it.