Syllogism for IBPS PO — All, Some, No Logic with Venn Diagrams

intermediate 18 min read

Concept

Syllogism is about drawing valid conclusions from a set of given statements — and crucially, only from those statements. You are not allowed to bring in real-world knowledge. "All politicians are honest" is a valid premise for this exercise even if you personally disagree with it.

The core vocabulary is three quantifiers:

Here is the analogy that makes this click. Think of sets as physical containers:

Your job in a syllogism question is to look at these boxes and decide: can I guarantee that this specific conclusion is true for every possible arrangement that fits the statements? If any valid arrangement breaks the conclusion, the conclusion does not follow.

This is the trap most people fall into — they pick the conclusion that seems most likely or most natural, rather than the one that is guaranteed by every valid arrangement. IBPS PO questions are specifically designed to exploit this. The "All computers are useful" type conclusion almost never follows, even when it feels like it should. The "Some machines are useful" type almost always does, because it only claims a partial overlap.

One more important concept: possibility vs. definite conclusions. Some questions ask whether a conclusion "possibly" follows rather than "definitely" follows. A possible conclusion is one that could be true in at least one valid Venn diagram arrangement — even if it is not guaranteed in all arrangements. Keep these two question types strictly separate in your head.


Deep Dive

The Four Statement Types and Their Conversions

The standard classification uses the letters A, E, I, O:

| Type | Form | Example | |------|------|---------| | A | All S are P | All cats are animals | | E | No S is P | No cat is a dog | | I | Some S are P | Some cats are black | | O | Some S are not P | Some cats are not black |

Conversion rules (these are valid flips):

Remember: "All books are papers" does NOT mean "All papers are books." It does mean "Some papers are books." This is the most frequently exploited gap in IBPS PO syllogism.

Chain Linking — The Core Skill

Most IBPS PO syllogism questions require you to chain two or three statements together to derive a new conclusion. Here are the productive chains:

Chain 1 (All + All → All): All A are B + All B are C → All A are C

Chain 2 (All + Some → Some, forward only): All A are B + Some B are C → No guaranteed conclusion about A and C Some A are B + All B are C → Some A are C (this one works)

Look — this is the exact trap in most questions. "All computers are machines. Some machines are electronic." You cannot conclude anything about computers and electronics because the "Some machines" may be a different subset entirely from the machines that are computers. Draw it out: computers sit inside machines, and the electronic overlap touches a separate part of machines.

Chain 3 (No + All → No, reverse): No A is B + All B are C → No A is C (via contrapositive) No A is B + All C are B → No A is C (also valid)

Chain 4 (Some + All → Some): Some A are B + All B are C → Some A are C (guaranteed)

This is the productive chain that appears in almost every IBPS PO question. Identify a "Some" statement linking to an "All" statement through a shared middle term, and you will get a "Some" conclusion at the other end.

The Venn Diagram Method (Definite Conclusions)

Draw the most "pessimistic" diagram — the one that gives the least overlap while still satisfying all statements. If the conclusion holds even in the most pessimistic valid drawing, it follows. If it fails, it does not follow.

For "All A are B, Some B are C":

For "Some A are B, All B are C":

Possibility Questions

When a question asks "which conclusion possibly follows," you draw the most "optimistic" diagram — any arrangement where the conclusion could be true without violating the given statements. If you can draw even one valid diagram where the conclusion holds, it possibly follows.

Example: "All A are B. Some B are C." Possibly, All A are C? Yes — you can draw A entirely inside the overlap of B and C. It is not guaranteed, but it is possible.

The "No" Statement and Contrapositive

"No A is B" is symmetric: it also means "No B is A." This is the only statement type that fully converts.

"No politician is honest" + "All honest people are trustworthy":


Memory Tricks & Shortcuts

patternSome-All Chain Lock

When you see "Some X are Y" followed by "All Y are Z" (Y is the shared middle term), the conclusion "Some X are Z" is always locked in. No need to draw anything.

Worked example: "Some doctors are engineers. All engineers are teachers." → Some doctors are teachers. Done in 3 seconds.

Standard Venn diagram method: 20-25 seconds. This pattern recognition: 3-4 seconds. Every question with this structure is a free point.

patternAll + Some = Blocked

When you see "All X are Y" followed by "Some Y are Z," you get nothing about X and Z. The "Some Y" might be the subset of Y that has no overlap with X.

Label this mentally: "All-then-Some = BLOCKED." If a conclusion attempts to connect X and Z here, eliminate it immediately.

Worked example: "All books are papers. Some papers are white." Conclusion "Some books are white" — blocked. Eliminated in 2 seconds vs. 15 seconds of Venn drawing.

eliminationNo + All Double Kill

"No A is B" + "All B are C" means "No A is C." Reason: Every C has come through B (since all B are C... wait — reverse direction). Actually apply it as: "No A is B" + "All C are B" → No A is C (since every C is a B, and no A is a B, no A is a C).

Alternatively: "No A is B" + "All B are C" → use contrapositive: if something is A, it cannot be B; if it is B, it must be C; since A cannot be B, A's relation to C is blocked.

Test: "No politician is honest. All honest are trustworthy." The No-statement kills any positive link between politicians and trustworthy. Conclusion I (No politician is trustworthy) follows. Pattern recognition: 5 seconds vs. 20 seconds drawing.

eliminationReverse Conversion Test

Before accepting a conclusion, mentally ask: is this just a valid conversion of a given statement? "Some papers are books" when told "All books are papers" — that is just a valid A→I conversion. Accept it immediately without drawing.

Conversely, "All papers are books" when told "All books are papers" — that is an invalid full flip of A-type. Reject in 2 seconds.

This saves you from the most common trap: candidates draw full Venn diagrams for conclusions that are either obvious conversions (accept instantly) or obvious invalid flips (reject instantly). Step count reduced from 6 steps to 1 step.

patternSome + No = Some Not

"Some A are B" + "No B is C" → "Some A are not C."

Those elements of A that are also B cannot be C (since No B is C). So at minimum, some A exist that are not C.

Worked example: "Some flowers are beautiful. No beautiful thing is ugly." → Some flowers are not ugly. This is conclusion II in the roses question — it follows directly. Pattern lock: 4 seconds. Drawing: 18 seconds.


Fast-Solving Framework

In the exam hall, run this decision tree in sequence:

Step 1 — Identify the middle term. The term shared between two statements is your chain link. Write it down: Statement 1 ends with X, Statement 2 starts with X. X is the middle term.

Step 2 — Check the chain type. Is it Some→All (productive), All→Some (blocked), All→All (productive), No→anything (kills positive links)?

Step 3 — Apply the chain rule. Derive the intermediate conclusion in 3 seconds using the patterns above. Write it alongside the statements.

Step 4 — Test each given conclusion. Ask: Is this conclusion guaranteed by my derived chain? Or is it just a possibility? If the question asks for definite conclusions, the conclusion must hold in every valid arrangement. If it asks for possible conclusions, it just needs to hold in one.

Step 5 — Use elimination on unlikely conclusions. If a conclusion says "All X are Z" but your chain only established "Some X are Z," reject it immediately. If the chain involved a "No" statement on the X-side, reject all positive conclusions involving X.

Time budget per question: 40-50 seconds. If you are drawing full Venn diagrams for every question, you are spending 90-120 seconds. The chain rules above cut that to under a minute.


Solved PYQs

Why this question: Tests the classic All→Some block trap combined with a productive Some→All chain.

Previous Year Questionपिछले वर्ष का प्रश्न
Statements: All athletes are fit. Some fit people are young. All young people are energetic. Conclusions: I. All athletes are energetic. II. Some fit people are energetic.
कथन: सभी खिलाड़ी फिट हैं। कुछ फिट लोग युवा हैं। सभी युवा लोग ऊर्जावान हैं। निष्कर्ष: I. सभी खिलाड़ी ऊर्जावान हैं। II. कुछ फिट लोग ऊर्जावान हैं।
  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Both conclusions I and II follow
  4. Neither conclusion I nor II follows
  1. केवल निष्कर्ष I सही है
  2. केवल निष्कर्ष II सही है
  3. निष्कर्ष I और II दोनों सही हैं
  4. न तो निष्कर्ष I और न ही II सही है
Solutionसमाधान
We cannot conclude that all athletes are energetic as we don't know if all athletes are young. However, from 'Some fit people are young' and 'All young people are energetic', we get 'Some fit people are energetic' (conclusion II follows).
सभी खिलाड़ी ऊर्जावान हैं यह नहीं कह सकते क्योंकि हमें नहीं पता कि सभी खिलाड़ी युवा हैं या नहीं। लेकिन 'कुछ स्वस्थ लोग युवा हैं' और 'सभी युवा लोग ऊर्जावान हैं' से 'कुछ स्वस्थ लोग ऊर्जावान हैं' निकलता है।

Solving path: Chain the statements. "All athletes are fit" + "Some fit people are young" — this is an All→Some chain. Blocked. Cannot conclude anything about athletes and young. So Conclusion I (All athletes are energetic) fails.

Now take the productive chain: "Some fit people are young" + "All young people are energetic" — this is Some→All. Locked. Conclusion: Some fit people are energetic. Conclusion II follows. Answer: Only II.


Why this question: Tests the No + All → No pattern using contrapositive reasoning.

Previous Year Questionपिछले वर्ष का प्रश्न
Statements: No politician is honest. All honest people are trustworthy. Some trustworthy people are reliable. Conclusions: I. No politician is trustworthy. II. Some reliable people are honest.
कथन: कोई भी नेता ईमानदार नहीं है। सभी ईमानदार लोग भरोसेमंद हैं। कुछ भरोसेमंद लोग विश्वसनीय हैं। निष्कर्ष: I. कोई भी नेता भरोसेमंद नहीं है। II. कुछ विश्वसनीय लोग ईमानदार हैं।
  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Both conclusions I and II follow
  4. Neither conclusion I nor II follows
  1. केवल निष्कर्ष I सही है
  2. केवल निष्कर्ष II सही है
  3. निष्कर्ष I और II दोनों सही हैं
  4. न तो निष्कर्ष I और न ही II सही है
Solutionसमाधान
From 'No politician is honest' and 'All honest people are trustworthy', we can conclude 'No politician is trustworthy' using contrapositive reasoning (conclusion I follows). We cannot establish the connection for conclusion II.
'कोई राजनेता ईमानदार नहीं है' और 'सभी ईमानदार लोग भरोसेमंद हैं' से विपरीत तर्क का उपयोग करके 'कोई राजनेता भरोसेमंद नहीं है' निकाल सकते हैं। निष्कर्ष II के लिए संबंध स्थापित नहीं कर सकते।

Solving path: "No politician is honest" — politicians and honest are completely separate boxes. "All honest people are trustworthy" — honest box sits inside trustworthy box. Since politicians have zero overlap with honest, and honest is what feeds trustworthy, politicians cannot reach trustworthy through any path. Conclusion I (No politician is trustworthy) follows.

For Conclusion II (Some reliable are honest): "Some trustworthy are reliable" is the chain — but this is the All→Some reverse direction and we only know Some trustworthy are reliable, not where honest sits relative to reliable. Cannot establish. Only I follows.


Why this question: Another All→Some block vs. Some→All productive chain — the most common IBPS PO pattern.

Previous Year Questionपिछले वर्ष का प्रश्न
Statements: All computers are machines. Some machines are electronic. All electronic items are useful. Conclusions: I. All computers are useful. II. Some machines are useful.
कथन: सभी कंप्यूटर मशीनें हैं। कुछ मशीनें इलेक्ट्रॉनिक हैं। सभी इलेक्ट्रॉनिक वस्तुएँ उपयोगी हैं। निष्कर्ष: I. सभी कंप्यूटर उपयोगी हैं। II. कुछ मशीनें उपयोगी हैं।
  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Both conclusions I and II follow
  4. Neither conclusion I nor II follows
  1. केवल निष्कर्ष I सही है
  2. केवल निष्कर्ष II सही है
  3. निष्कर्ष I और II दोनों सही हैं
  4. न तो निष्कर्ष I और न ही II सही है
Solutionसमाधान
We cannot conclude that all computers are useful as we don't know if all computers are electronic. However, from 'Some machines are electronic' and 'All electronic items are useful', we get 'Some machines are useful' (conclusion II follows).
सभी कंप्यूटर उपयोगी हैं यह नहीं कह सकते क्योंकि हमें नहीं पता कि सभी कंप्यूटर इलेक्ट्रॉनिक हैं या नहीं। लेकिन 'कुछ मशीनें इलेक्ट्रॉनिक हैं' और 'सभी इलेक्ट्रॉनिक वस्तुएं उपयोगी हैं' से 'कुछ मशीनें उपयोगी हैं' निकलता है।

Solving path: "All computers are machines" + "Some machines are electronic" — All→Some, blocked. Conclusion I (All computers are useful) fails.

"Some machines are electronic" + "All electronic items are useful" — Some→All, locked. Some machines are useful. Conclusion II follows. Answer: Only II.


Why this question: Identical structure to the above — tests whether you have the pattern locked or are re-deriving each time.

Previous Year Questionपिछले वर्ष का प्रश्न
Statements: All books are papers. Some papers are white. All white things are clean. Conclusions: I. All books are clean. II. Some papers are clean.
कथन: सभी किताबें कागज हैं। कुछ कागज सफेद हैं। सभी सफेद चीजें साफ हैं। निष्कर्ष: I. सभी किताबें साफ हैं। II. कुछ कागज साफ हैं।
  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Both conclusions I and II follow
  4. Neither conclusion I nor II follows
  1. केवल निष्कर्ष I सही है
  2. केवल निष्कर्ष II सही है
  3. निष्कर्ष I और II दोनों सही हैं
  4. न तो निष्कर्ष I और न ही II सही है
Solutionसमाधान
We cannot conclude that all books are clean as we don't know if all books are white. However, from 'Some papers are white' and 'All white things are clean', we get 'Some papers are clean' (conclusion II follows).
सभी किताबें साफ हैं यह नहीं कह सकते क्योंकि हमें नहीं पता कि सभी किताबें सफेद हैं या नहीं। लेकिन 'कुछ कागज़ सफेद हैं' और 'सभी सफेद चीज़ें साफ हैं' से 'कुछ कागज़ साफ हैं' निकलता है।

Solving path: "All books are papers" + "Some papers are white" — All→Some, blocked. "All books are clean" fails.

"Some papers are white" + "All white things are clean" — Some→All, locked. Some papers are clean. Conclusion II follows. Answer: Only II.


Why this question: Three-statement chain requiring you to identify which link is productive and which is not.

Previous Year Questionपिछले वर्ष का प्रश्न
Statements: Some doctors are engineers. All engineers are teachers. Some teachers are lawyers. Conclusions: I. Some doctors are teachers. II. Some lawyers are engineers.
कथन: कुछ डॉक्टर इंजीनियर हैं। सभी इंजीनियर टीचर हैं। कुछ टीचर वकील हैं। निष्कर्ष: I. कुछ डॉक्टर टीचर हैं। II. कुछ वकील इंजीनियर हैं।
  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Both conclusions I and II follow
  4. Neither conclusion I nor II follows
  1. केवल निष्कर्ष I सही है
  2. केवल निष्कर्ष II सही है
  3. निष्कर्ष I और II दोनों सही हैं
  4. न तो निष्कर्ष I और न ही II सही है
Solutionसमाधान
From 'Some doctors are engineers' and 'All engineers are teachers', we get 'Some doctors are teachers' (conclusion I follows). Conclusion II cannot be established as the relationship between lawyers and engineers is not definite.
'कुछ डॉक्टर इंजीनियर हैं' और 'सभी इंजीनियर शिक्षक हैं' से 'कुछ डॉक्टर शिक्षक हैं' निष्कर्ष I सही है। निष्कर्ष II स्थापित नहीं हो सकता क्योंकि वकीलों और इंजीनियरों के बीच संबंध निश्चित नहीं है।

Solving path: "Some doctors are engineers" + "All engineers are teachers" — Some→All, locked. Some doctors are teachers. Conclusion I follows.

For Conclusion II (Some lawyers are engineers): "All engineers are teachers" + "Some teachers are lawyers" — this is All→Some reversed. The Some teachers who are lawyers may not overlap with the teachers who came from engineers. Cannot conclude. Only I follows.


Why this question: Tests the Some + No = Some-Not pattern and the All→Some block.

Previous Year Questionपिछले वर्ष का प्रश्न
Statements: All roses are flowers. Some flowers are beautiful. No beautiful thing is ugly. Conclusions: I. Some roses are beautiful. II. Some flowers are not ugly.
कथन: सभी गुलाब फूल हैं। कुछ फूल सुंदर हैं। कोई भी सुंदर चीज़ बदसूरत नहीं है। निष्कर्ष: I. कुछ गुलाब सुंदर हैं। II. कुछ फूल बदसूरत नहीं हैं।
  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Both conclusions I and II follow
  4. Neither conclusion I nor II follows
  1. केवल निष्कर्ष I सही है
  2. केवल निष्कर्ष II सही है
  3. निष्कर्ष I और II दोनों सही हैं
  4. न तो निष्कर्ष I और न ही II सही है
Solutionसमाधान
Conclusion I cannot be established as we don't know if roses are among the beautiful flowers. From 'Some flowers are beautiful' and 'No beautiful thing is ugly', we get 'Some flowers are not ugly' (conclusion II follows).
निष्कर्ष I स्थापित नहीं हो सकता क्योंकि हम नहीं जानते कि गुलाब सुंदर फूलों में से हैं या नहीं। 'कुछ फूल सुंदर हैं' और 'कोई सुंदर चीज बदसूरत नहीं है' से 'कुछ फूल बदसूरत नहीं हैं' निष्कर्ष II सही है।

Solving path: "All roses are flowers" + "Some flowers are beautiful" — All→Some, blocked. Cannot conclude "Some roses are beautiful." Conclusion I fails.

"Some flowers are beautiful" + "No beautiful thing is ugly" — Some→No produces Some-Not. Some flowers are not ugly. Conclusion II follows. Answer: Only II.


Why this question: Tests your ability to resist "obvious-sounding" Conclusion I while confirming a three-step Some→All chain.

Previous Year Questionपिछले वर्ष का प्रश्न
Statements: No politician is honest. Some honest people are rich. All rich people are happy. Conclusions: I. Some politicians are not rich. II. Some happy people are honest.
कथन: कोई भी नेता ईमानदार नहीं है। कुछ ईमानदार लोग अमीर हैं। सभी अमीर लोग खुश हैं। निष्कर्ष: I. कुछ नेता अमीर नहीं हैं। II. कुछ खुश लोग ईमानदार हैं।
  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Both conclusions I and II follow
  4. Neither conclusion I nor II follows
  1. केवल निष्कर्ष I सही है
  2. केवल निष्कर्ष II सही है
  3. निष्कर्ष I और II दोनों सही हैं
  4. न तो निष्कर्ष I और न ही II सही है
Solutionसमाधान
Conclusion I cannot be definitively established from the given statements. From 'Some honest people are rich' and 'All rich people are happy', we get 'Some happy people are honest' (conclusion II follows).
दिए गए कथनों से निष्कर्ष I निश्चित रूप से स्थापित नहीं हो सकता। 'कुछ ईमानदार लोग अमीर हैं' और 'सभी अमीर लोग खुश हैं' से 'कुछ खुश लोग ईमानदार हैं' निष्कर्ष II सही है।

Solving path: Conclusion I says "Some politicians are not rich." "No politician is honest" tells you politicians cannot be honest. But rich and honest are not the same — some honest people are rich (Some→All linking honest to rich to happy), but politicians might still be rich through a different path not mentioned. Cannot establish that politicians are not rich. Conclusion I is tempting but does not definitively follow.

"Some honest people are rich" + "All rich people are happy" — Some→All, locked. Some honest people are happy. By conversion (I-type, symmetric): Some happy people are honest. Conclusion II follows. Answer: Only II.


Why this question: Clean repeat of the core IBPS PO pattern — confirms you are applying the chain rules automatically.

Previous Year Questionपिछले वर्ष का प्रश्न
Statements: All mangoes are fruits. Some fruits are sweet. No sweet thing is bitter. Conclusions: I. All mangoes are sweet. II. Some fruits are not bitter.
कथन: सभी आम फल हैं। कुछ फल मीठे हैं। कोई भी मीठी चीज़ कड़वी नहीं है। निष्कर्ष: I. सभी आम मीठे हैं। II. कुछ फल कड़वे नहीं हैं।
  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Both conclusions I and II follow
  4. Neither conclusion I nor II follows
  1. केवल निष्कर्ष I सही है
  2. केवल निष्कर्ष II सही है
  3. निष्कर्ष I और II दोनों सही हैं
  4. न तो निष्कर्ष I और न ही II सही है
Solutionसमाधान
Conclusion I cannot be established as we don't know if all mangoes are among the sweet fruits. From 'Some fruits are sweet' and 'No sweet thing is bitter', we get 'Some fruits are not bitter' (conclusion II follows).
निष्कर्ष I स्थापित नहीं हो सकता क्योंकि हम नहीं जानते कि सभी आम मीठे फलों में से हैं या नहीं। 'कुछ फल मीठे हैं' और 'कोई मीठी चीज कड़वी नहीं है' से 'कुछ फल कड़वे नहीं हैं' निष्कर्ष II सही है।

Solving path: "All mangoes are fruits" + "Some fruits are sweet" — All→Some, blocked. "All mangoes are sweet" fails.

"Some fruits are sweet" + "No sweet thing is bitter" — Some→No produces Some-Not. Some fruits are not bitter. Conclusion II follows. Answer: Only II.


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