Syllogism: Two and Three Statements, Definite Conclusions
Syllogism: Two and Three Statements, Definite Conclusions
A syllogism gives statements with "all", "some" and "no", and asks which conclusions must follow. Treat the statements as true even if they sound absurd, and accept a conclusion only if it is true in every possible diagram. Two tools settle every question: the combination table and the conversion rules, with a quick Venn sketch to check.
1. Combination Table (first statement links A to B, second links B to C)
| Statement 1 | Statement 2 | Definite conclusion |
|---|---|---|
| All A are B | All B are C | All A are C |
| All A are B | No B is C | No A is C |
| Some A are B | All B are C | Some A are C |
| Some A are B | No B is C | Some A are not C |
| No A is B | All B are C | Some C are not A |
| All A are B | Some B are C | No definite conclusion |
| Some A are B | Some B are C | No definite conclusion |
2. Conversion Rules
| Statement | Valid conversion |
|---|---|
| All A are B | Some B are A |
| Some A are B | Some B are A |
| No A is B | No B is A |
| Some A are not B | No conversion |
The middle term (B) must link the two statements; rearrange the order of statements if needed
"Consider the statements to be true even if they seem to be at variance with commonly known facts": never use real-world knowledge
✗ All A are B and some B are C, so some A are C | ✓ The C part of B may lie outside A: no definite conclusion
✗ All fish are birds is false, so ignore it | ✓ Treat every statement as true, however odd
हिंदी नोट: न्यायवाक्य में कथनों को सत्य मानिए, भले ही वे सामान्य ज्ञान के विपरीत हों। निष्कर्ष तभी सही है जब हर संभव वेन आरेख में सत्य हो। "सभी A, B हैं" का रूपांतरण "कुछ B, A हैं" होता है।
Exam Pointer: Verified NTPC patterns: two statements with "all" and "some" conclusions (January 2021 CBT-1, January 2017 CBT-2), three statements (March 2026 Graduate CBT-1), statements at variance with common sense (December 2020 CBT-1) and two statements with four numbered conclusions (January 2017 CBT-2).
Pariksha Pattern: Every Way NTPC Asks This Topic
Pattern 1: Two statements, two or three conclusions
[PYQ: NTPC CBT-1 16-Jan-2021 Shift-2 | NTPC CBT-2 19-Jan-2017 Shift-3]
EXAM LEVEL
Q. Statements: All pens are books. All books are tables. Conclusions: I. All pens are tables. II. Some tables are pens. Which follow?
All + All gives "All pens are tables" (I). Converting it gives "Some tables are pens" (II).
Answer: Both I and II
EXAMATLAS LEVEL
Q. Statements: Some cats are dogs. No dog is a rat. Conclusions: I. Some cats are not rats. II. All cats are rats. III. Some rats are cats. Which follow?
Some + No gives "Some cats are not rats" (I), so II, which contradicts I, fails. The cats that are not dogs may or may not be rats, so III is not certain.
Answer: Only I
Pattern 2: Three statements
[PYQ: NTPC Graduate CBT-1 22-Mar-2026 Shift-3]
EXAM LEVEL
Q. Statements: All A are B. No B is C. Some C are D. Conclusions: I. No A is C. II. Some D are not B. Which follow?
All A are B + No B is C gives No A is C (I). Some C are D converts to Some D are C, and those D, being C, are not B: Some D are not B (II).
Answer: Both I and II
EXAMATLAS LEVEL
Q. Statements: Some X are Y. All Y are Z. No Z is W. Conclusions: I. Some X are Z. II. Some X are not W. III. No Y is W. IV. Some W are X. Which follow?
Some X are Y + All Y are Z gives I. Those X are Z, and no Z is W, so II follows. All Y are Z + No Z is W gives No Y is W (III). The X that are not Y may or may not be W, so IV is not certain.
Answer: I, II and III
Pattern 3: Statements at variance with common sense
[PYQ: NTPC CBT-1 28-Dec-2020 Shift-2]
EXAM LEVEL
Q. Statements: All fish are birds. Some birds are trees. Conclusions: I. Some fish are trees. II. Some birds are fish. Which follow?
All + Some gives no definite link between fish and trees, so I fails. All fish are birds converts to Some birds are fish (II).
Answer: Only II
EXAMATLAS LEVEL
Q. Statements: All mangoes are chairs. No chair is a river. Some rivers are hills. Conclusions: I. No mango is a river. II. Some hills are not chairs. III. Some hills are mangoes. Which follow?
All + No gives I. Some rivers are hills converts to Some hills are rivers, and rivers are never chairs, so II follows. Hills that are rivers cannot be mangoes, and other hills are unknown, so III is not certain.
Answer: I and II
Pattern 4: Four numbered conclusions: pick the valid set
[PYQ: NTPC CBT-2 18-Jan-2017 Shift-3]
EXAM LEVEL
Q. Statements: Some red are black. All black are white. Conclusions: I. Some red are white. II. Some white are black. III. All white are red. IV. No red is white. Which follow?
Some + All gives I. All black are white converts to II. III cannot be inferred, and IV contradicts I.
Answer: I and II
EXAMATLAS LEVEL
Q. Statements: No P is Q. All Q are R. Some R are S. Conclusions: I. Some R are not P. II. Some S are Q. III. No P is R. IV. Some Q are not P. Which follow?
No + All gives Some R are not P (I), namely the R that are Q. Since no Q is P, Some Q are not P (IV). II needs the S part of R to overlap Q, which is not certain; III is not certain either, since P may still meet R outside Q.
Answer: I and IV
60-Second Revision
- Learn the seven-row combination table.
- All converts to Some; Some and No convert both ways; Some-not does not convert.
- All + Some and Some + Some give no definite link.
- Treat odd statements as true; never use outside knowledge.