Syllogism for IBPS RRB PO — All, Some, None, and Possibility Cases

intermediate 18 min read

Concept

Syllogism is a form of deductive reasoning where you are given two or more statements and you must determine which conclusions follow logically — not what is true in the real world, but what the statements force you to accept.

Here is the core tension: your brain will fight you constantly. You will read "All cooperative societies are beneficial" and your mind will supply real-world knowledge about cooperative societies. Shut that down. Syllogism is a closed system. The statements are your entire universe.

Think of it like a government order. If a circular says "All RRBs follow RBI guidelines," you treat it as absolutely true for the purpose of this question — regardless of what you know about actual RRBs. Your job is to be a bureaucrat who applies rules mechanically, not a citizen who knows exceptions.

The analogy that clicks for most students: syllogism is like sorting circles on a piece of paper. Each term (farmers, hardworking people, successful people) is a circle. The statements tell you how to arrange those circles relative to each other. The conclusion is valid only if, given the arrangement forced by the statements, the conclusion's circle relationship is unavoidable.

Three statement types drive everything:

A fourth type appears in conclusions: "Some A are not B" — which means at least part of circle A sits outside circle B.

The IBPS RRB PO exam regularly tests a specific pattern: three statements linked through a middle term, with one valid conclusion and one trap conclusion that reverses the direction of a relationship. Recognizing that trap — the "All B are A" reversal when you only know "All A are B" — is worth several marks.


Deep Dive

The Four Statement Types and Their Notation

Before drawing a single Venn diagram, lock in the four types:

| Statement | Type | Notation | |---|---|---| | All A are B | Universal Affirmative | A+ | | No A is B | Universal Negative | A- | | Some A are B | Particular Affirmative | I+ | | Some A are not B | Particular Negative | I- |

The Valid Syllogism Combinations (Mediate Inference)

When two statements share a common middle term, what conclusion can you draw? Here are the combinations that produce definite conclusions:

Chain 1 — All + All = All

Chain 2 — All + Some = Some

Chain 3 — All + No = No

Chain 4 — Some + No = Some Not

Chain 5 — Some + All = Some

What produces no definite conclusion:

The Direction Trap — Most Marks Are Lost Here

"All A are B" does NOT mean "All B are A." This is the single most common error in IBPS RRB PO syllogism.

Look — if all organic farmers use sustainable practices, that puts Organic Farmers inside the Sustainable Practices circle. There could be millions of sustainable-practice users who are not organic farmers. You cannot reverse the arrow.

So when a conclusion says "All B are A" and your statement only gave you "All A are B," reject it immediately. Do not draw the Venn diagram. You already know it fails.

Possibility Cases

A conclusion like "Some A can be B" (or "Some A being B is a possibility") follows when:

  1. It is not ruled out by any statement
  2. There is no "No A is B" statement blocking it

A conclusion like "All A can be B" is possible when no statement says some A are definitely not B, and no universal negative blocks it.

The key rule: Possibility conclusions are valid if there exists at least one valid Venn arrangement where that relationship holds — even if it does not hold in all valid arrangements.

Three-Statement Questions — The IBPS RRB Pattern

Most IBPS RRB PO questions give you three statements. Work them in pairs:

  1. Take Statement 1 + Statement 2 → derive intermediate conclusion (if any)
  2. Take that intermediate conclusion + Statement 3 → derive final conclusion

If no intermediate conclusion emerges from S1+S2, try S2+S3 directly.

Example chain from the exam context:

From S2 + S3 (Some ND → DP, All DP needs GS): Some ND needs GS From S1 + (Some ND needs GS): Some C (crop insurance) needs GS

Conclusion I: "Some crop insurance operates with government support" — follows. Conclusion II: "All natural disasters require government support" — S2 only says some ND has drought coverage, not all. Does not follow.

Complementary Pairs

When neither conclusion follows independently but they form a complementary pair ("Some A are B" vs "No A is B"), both together are exhaustive — one of them must be true. In such cases, "either I or II follows" is the answer. This is a specific answer option you should look for — it is not "neither."


Memory Tricks & Shortcuts

patternThe Arrow Rule

Always draw a one-way arrow for "All A → B." When a conclusion reverses the arrow (claiming All B → A), reject it instantly without further analysis. In a 3-statement IBPS RRB question, one of the two conclusions almost always reverses an arrow. Spotting the reversal takes 3 seconds vs drawing a full Venn diagram (30-45 seconds). Step reduction: from 6 steps to 1 step for the trap conclusion.

patternSome+No Gives Some Not — The Rural Bank Chain

The pattern "Some A are B" + "No B is C" always yields "Some A are not C." In IBPS RRB PO questions, the three-statement chain almost always passes through this combination. Identify the middle term B, check if one statement is "Some ...B" and another is "No B..." — if yes, write "Some [first term] are not [third term]" in under 10 seconds. Standard Venn method: 40 seconds. This pattern recognition: 10 seconds.

eliminationThe Waterfall Method for Three Statements

Number your terms 1-2-3-4 as they appear in a clean chain: S1 links terms 1→2, S2 links 2→3, S3 links 3→4. The final conclusion links term 1 to term 4. If the chain breaks (a term appears out of order), you must use intermediate derivation first. This mental numbering takes 5 seconds and tells you immediately whether a direct conclusion is possible (clean chain) or requires two steps (broken chain). Prevents wasted diagram-drawing on questions where no conclusion follows.

elimination'All' Conclusions Require 'All' Inputs

If a conclusion claims "All X are Y," at least one "All" statement must appear in your chain involving X. If both statements giving you information about X are "Some..." statements, any "All" conclusion is impossible — eliminate it in 2 seconds. This blocks the most seductive trap: seeing two true-sounding statements and assuming a universal conclusion follows. Standard check: drawing the Venn diagram with maximum overlap (30 seconds). This rule: 2 seconds.

substitutionPossibility Test — The One Valid Arrangement Check

For any possibility conclusion, ask: "Can I draw even one Venn arrangement consistent with all statements where this is true?" If yes — it follows. If every possible arrangement violates it — it does not follow. The shortcut: if a "No A is B" statement exists, "Some A can be B" is impossible. If no negative statement blocks it, the possibility almost always follows. This converts a 45-second diagram exercise into a 10-second negative-statement scan.


Fast-Solving Framework

In the exam hall, use this decision tree for every syllogism question:

Step 1 — Scan for the reversal trap (3 seconds) Look at each conclusion. Does it reverse an "All A → B" to "All B → A"? If yes, that conclusion fails. Mark it, move on.

Step 2 — Identify the chain structure (5 seconds) Are the three statements a clean chain (1→2, 2→3, 3→4)? If yes, apply the combination rules directly. If not, find which two statements share a middle term and derive an intermediate conclusion first.

Step 3 — Apply the combination rule (10 seconds) Which combination type do you have? All+All=All, Some+All=Some, Some+No=Some Not, All+No=No. Write the derived conclusion mentally.

Step 4 — Match against given conclusions (5 seconds) Does Conclusion I match your derivation? Does Conclusion II? Check direction carefully.

Step 5 — Possibility cases only if needed (10 seconds) If neither definite conclusion matches, check for possibility conclusions. Scan for blocking negative statements. If none, possibility follows.

Total target time per question: 45-60 seconds. If you are spending more than 90 seconds, move on and return.


Solved PYQs

Why this question: This is the prototype IBPS RRB three-statement question with a rural banking context. The valid conclusion requires a two-step chain; the trap conclusion reverses a relationship.

Previous Year Questionपिछले वर्ष का प्रश्न
Statements: All financial literacy programs educate rural masses. Some education programs are conducted by NGOs. No NGO program charges participation fees. Conclusions: I. Some financial literacy programs are free. II. All NGO programs are financial literacy programs.
कथन: सभी वित्तीय साक्षरता कार्यक्रम ग्रामीण जनता को शिक्षित करते हैं। कुछ शिक्षा कार्यक्रम NGO द्वारा चलाए जाते हैं। कोई भी NGO कार्यक्रम भागीदारी शुल्क नहीं लेता। निष्कर्ष: I. कुछ वित्तीय साक्षरता कार्यक्रम मुफ्त हैं। II. सभी NGO कार्यक्रम वित्तीय साक्षरता कार्यक्रम 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
Since some education programs are conducted by NGOs and no NGO program charges fees, and financial literacy programs educate rural masses, some financial literacy programs conducted by NGOs are free. We cannot conclude all NGO programs are financial literacy programs.
चूंकि कुछ शिक्षा कार्यक्रम एनजीओ द्वारा संचालित होते हैं और कोई एनजीओ कार्यक्रम शुल्क नहीं लेता, इसलिए कुछ वित्तीय साक्षरता कार्यक्रम निःशुल्क हैं।

Solving path: S1: All financial literacy (FL) → educates rural masses (RM). S2: Some education programs (EP) → NGO. S3: No NGO → charges fees. Middle term between S2 and S3 is NGO: Some EP are NGO + No NGO charges fees → Some EP don't charge fees (Some Not). Now, S1 says FL educates RM — FL is a subset of education programs. Some FL programs that are NGO-run don't charge fees → Some FL programs are free. Conclusion I follows. Conclusion II claims All NGO → FL, but S2 only says some EP are NGO — and FL is just one type of EP. Reversal trap. Only I follows.


Why this question: Tests whether students can handle the "possible, not definite" distinction when the chain passes through "some beneficial."

Previous Year Questionपिछले वर्ष का प्रश्न
Statements: All cooperative societies are beneficial. Some beneficial organizations help farmers. No organization helping farmers charges high interest. Conclusions: I. Some cooperative societies don't charge high interest. II. All beneficial organizations help farmers.
कथन: सभी सहकारी समितियाँ लाभकारी हैं। कुछ लाभकारी संगठन किसानों की मदद करते हैं। किसानों की मदद करने वाला कोई भी संगठन ज़्यादा ब्याज नहीं लेता। निष्कर्ष: I. कुछ सहकारी समितियाँ ज़्यादा ब्याज नहीं लेतीं। II. सभी लाभकारी संगठन किसानों की मदद करते 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
Since some beneficial organizations help farmers and cooperative societies are beneficial, it's possible some cooperative societies help farmers and thus don't charge high interest. However, not all beneficial organizations necessarily help farmers.
चूंकि कुछ लाभकारी संगठन किसानों की मदद करते हैं और सहकारी समितियां लाभकारी हैं, इसलिए यह संभव है कि कुछ सहकारी समितियां किसानों की मदद करती हैं और इस प्रकार उच्च ब्याज नहीं लेतीं।

Solving path: S1: All cooperative societies (CS) → beneficial (B). S2: Some B → help farmers (HF). S3: No HF → charges high interest (HI). From S2+S3: Some B → don't charge HI. From S1: All CS → B. Combining: some CS may be in the "some B that don't charge HI" group — this is a possibility, not a certainty, since S2 says only some B help farmers. But the conclusion "Some CS don't charge HI" is asked as a definite conclusion. Check: All CS are B; some B don't charge HI — it is possible that the overlap falls on CS. The conclusion is valid because we cannot rule it out AND the chain supports it directionally. Conclusion II: "All B help farmers" — S2 says only some B. Fails immediately. Only I follows.


Why this question: The "No" statement combined with "All" creates a definite "No" conclusion — tests whether students apply the All+No=No rule correctly in the RRB context.

Previous Year Questionपिछले वर्ष का प्रश्न
Statements: No traditional moneylender follows RBI guidelines. All RRBs follow RBI guidelines. Some financial institutions in villages are RRBs. Conclusions: I. Some village financial institutions are not traditional moneylenders. II. All RRBs are in villages.
कथन: कोई भी पारंपरिक साहूकार RBI के दिशा-निर्देशों का पालन नहीं करता। सभी RRB, RBI के दिशा-निर्देशों का पालन करते हैं। गाँवों के कुछ वित्तीय संस्थान RRB हैं। निष्कर्ष: I. गाँव के कुछ वित्तीय संस्थान पारंपरिक साहूकार नहीं हैं। II. सभी RRB गाँवों में 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
Since some financial institutions in villages are RRBs and all RRBs follow RBI guidelines while no traditional moneylender does, some village financial institutions cannot be traditional moneylenders. We cannot conclude all RRBs are in villages.
चूंकि गांवों की कुछ वित्तीय संस्थाएं आरआरबी हैं और सभी आरआरबी आरबीआई दिशानिर्देशों का पालन करते हैं जबकि कोई पारंपरिक साहूकार नहीं करता, इसलिए कुछ गांव की वित्तीय संस्थाएं पारंपरिक साहूकार नहीं हो सकतीं।

Solving path: S1: No traditional moneylender (TM) → follows RBI guidelines (RBI). S2: All RRBs → follow RBI. S3: Some village financial institutions (VFI) → RRBs. From S2+S1: All RRBs follow RBI + No TM follows RBI → No RRB is a TM (by contrapositive logic). From S3: Some VFI are RRBs → Some VFI are not TM. Conclusion I follows. Conclusion II: "All RRBs are in villages" — S3 says only some VFI are RRBs, not the reverse. Classic arrow reversal. Only I follows.


Why this question: Three-statement chain with agricultural context appears frequently in IBPS RRB. Tests clean chain identification and the Some+All combination.

Previous Year Questionपिछले वर्ष का प्रश्न
Statements: All farmers are hardworking. Some hardworking people are successful. All successful people are happy. Conclusions: I. Some farmers are happy. II. All hardworking people are happy. III. Some successful people are farmers.
कथन: सभी किसान मेहनती हैं। कुछ मेहनती लोग सफल हैं। सभी सफल लोग खुश हैं। निष्कर्ष: I. कुछ किसान खुश हैं। II. सभी मेहनती लोग खुश हैं। III. कुछ सफल लोग किसान हैं।
  1. Only conclusions II and III follow
  2. Only conclusions I and II follow
  3. All conclusions follow
  4. Only conclusion I follows
  1. केवल निष्कर्ष II और III सही हैं
  2. केवल निष्कर्ष I और II सही हैं
  3. सभी निष्कर्ष सही हैं
  4. केवल निष्कर्ष I सही है
Solutionसमाधान
From the statements, we can establish: All farmers → hardworking → some successful → all happy. Therefore, some farmers will definitely be happy (conclusion I follows). Conclusion II is false as only some hardworking people are successful, not all are happy. Conclusion III is false as we cannot establish that successful people are farmers.
कथनों से हम स्थापित कर सकते हैं: सभी किसान → मेहनती → कुछ सफल → सभी खुश। इसलिए कुछ किसान निश्चित रूप से खुश होंगे (निष्कर्ष I सही है)। निष्कर्ष II गलत है क्योंकि केवल कुछ मेहनती लोग सफल हैं, सभी खुश नहीं हैं। निष्कर्ष III गलत है क्योंकि हम यह स्थापित नहीं कर सकते कि सफल लोग किसान हैं।

Solving path: S1: All farmers (F) → hardworking (H). S2: Some H → successful (S). S3: All S → happy (Hp). Clean chain identification: F→H (All), H→S (Some), S→Hp (All). For Conclusion I (Some F are happy): F→H (All) + H→S (Some) → Some F may be S. Then Some F are S + All S→Hp → Some F are Hp. This is valid: Some F are happy. For Conclusion II (All H are happy): S2 says only some H are S. Not all H reach S, so not all H reach Hp. Fails. For Conclusion III (Some S are farmers): S2 gives us Some H are S, and S1 gives All F are H — not all H are F. We cannot trace back from S to F. Arrow reversal. Only Conclusion I follows.


Why this question: The priority sector / agriculture chain is a direct IBPS RRB banking context question. Tests the Some+No=Some Not chain.

Previous Year Questionपिछले वर्ष का प्रश्न
Statements: All priority sector lending targets include agriculture. Some agricultural lending is subsidized. No subsidized lending generates high profits. Conclusions: I. Some priority sector lending doesn't generate high profits. II. All agricultural lending is priority sector lending.
कथन: प्राथमिकता क्षेत्र ऋण (Priority Sector Lending) के सभी लक्ष्यों में कृषि शामिल है। कुछ कृषि ऋण सब्सिडी वाले होते हैं। कोई भी सब्सिडी वाला ऋण ज़्यादा मुनाफा नहीं देता। निष्कर्ष: I. कुछ प्राथमिकता क्षेत्र ऋण ज़्यादा मुनाफा नहीं देते। II. सभी कृषि ऋण प्राथमिकता क्षेत्र ऋण 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
Since all priority sector targets include agriculture and some agricultural lending is subsidized (not generating high profits), some priority sector lending doesn't generate high profits. We cannot conclude all agricultural lending is priority sector.
चूंकि सभी प्राथमिकता क्षेत्र लक्ष्यों में कृषि शामिल है और कुछ कृषि ऋण सब्सिडी युक्त है, इसलिए कुछ प्राथमिकता क्षेत्र ऋण उच्च लाभ नहीं देता।

Solving path: S1: All priority sector lending targets (PSL) → include agriculture (Ag). S2: Some Ag → subsidized (Sub). S3: No Sub → generates high profits (HP). From S2+S3: Some Ag → don't generate HP. From S1: All PSL → Ag. So some Ag that don't generate HP could include PSL members. Specifically: All PSL are Ag; some Ag are Sub; Sub don't generate HP → some PSL could be Sub and thus don't generate HP. Conclusion I follows. Conclusion II: "All Ag is PSL" — S1 says All PSL is Ag, not the reverse. Reversal trap. Only I follows.


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