Statement & Conclusions for SSC MTS — Complete Logic Rules Guide

intermediate 18 min read

Concept

Statement and Conclusions questions give you two or more factual statements and ask which of the given conclusions must follow from those statements alone — not from common knowledge, not from opinion, but strictly from the logic in the statements.

Here is the core idea: you are playing a referee, not a judge. Your job is not to decide whether the statements are true in the real world. Your job is to decide whether a conclusion is compelled by the statements. If the statements could be true without the conclusion being true, the conclusion does not follow.

Think of it like a closed room. The statements are the only furniture in that room. A valid conclusion must already be sitting inside the room — built from what the statements gave you. If you have to bring in outside furniture (world knowledge, common sense, assumptions), the conclusion does not follow.

A quick analogy: Imagine you are given two boxes. Box A: "All cats are animals." Box B: "Some animals are friendly." Now someone asks — "Does it follow that some cats are friendly?" No. The friendly animals in Box B might be dogs, not cats. There is no guaranteed overlap. You cannot conclude it.

This topic is essentially applied syllogism — the formal study of what conclusions can be drawn from categorical statements. The four types of statements you will encounter are:

Every SSC MTS question on this topic will use one or more of these four types. Once you learn the rules for combining and converting them, this becomes a fast and reliable scoring topic.


Deep Dive

The Conversion Rule — Your Most Powerful Tool

Conversion means flipping the subject and predicate of a statement. Not every statement converts in the same way. Here are the exact rules:

| Original Statement | Converted Statement | Type Change | |---|---|---| | All S are P | Some P are S | A → I | | No S is P | No P is S | E → E | | Some S are P | Some P are S | I → I | | Some S are not P | Cannot be converted | O → X |

Look — this table alone solves about 40% of the questions you will face. Memorise the first three rows.

Why does "All S are P" become "Some P are S" and not "All P are S"?

Because if all cats are animals, it does not mean all animals are cats. But it does mean at least some animals (those that are cats) are cats. So you lose universality — All becomes Some — when you flip a Universal Affirmative.

The Chain Rule — Combining Two Statements

When you have two statements and want to draw a conclusion about the extreme terms (the two terms that are not shared), you use the middle term as a bridge. The rules are:

  1. All + All → All All A are B. All B are C. → All A are C.

  2. All + Some → Some (in the direction of "Some") All A are B. Some B are C. → No definite conclusion about A and C. But: Some A are B. All B are C. → Some A are C.

  3. Some + Some → No conclusion Some A are B. Some B are C. → Nothing about A and C.

  4. No + All → No (reversed) No A is B. All C are B. → No C is A. (or equivalently, No A is C.)

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

  6. All + No → No All A are B. No B is C. → No A is C.

The "Possibility" Trap

SSC MTS increasingly uses conclusions phrased as possibilities: "Some X being Y is a possibility." A possibility conclusion is valid unless the statements directly contradict it. If the statements say "No A is B," then "Some A are B is a possibility" does not follow. But if the statements are silent about the relationship, a possibility can follow.

Here is the rule: A possibility is true unless the combined statements make it impossible (i.e., a definite negative conclusion applies).

The Complementary Pair (Either-Or)

When two conclusions are exact opposites — one says "Some A are B" and the other says "No A is B" — and neither follows on its own, but together they cover all logical cases, the answer is "Either I or II follows." This is less common in SSC MTS but worth recognising.

Venn Diagram vs. Rules

Many candidates try to draw Venn diagrams for every question. That works but is slow. For straightforward questions (2 statements, 2 conclusions), the conversion table and chain rules above are faster. Use Venn diagrams only when you have three or more statements with complex interactions — reserve it as a backup, not your primary method.


Memory Tricks & Shortcuts

patternAEIS — The Conversion Code

Memorise the pattern: A→I, E→E, I→I, O→X (O never converts).

Worked example: "All Players are Singers" (A-type). Convert: "Some Singers are Players" (I-type). Done in 3 seconds.

Standard method (drawing Venn diagrams to verify): 20 seconds. This pattern lookup: 3 seconds.

eliminationSome+Some = Dead End

Whenever both linking statements are I-type ("Some A are B" and "Some B are C"), immediately eliminate any conclusion about A and C. You know with certainty that no definite conclusion about the extreme terms can follow.

Worked example: "Some tablets are laptops. Some laptops are computers." Any conclusion connecting tablets to computers directly? Kill it. Two "Some" links give you nothing. This saves you from drawing diagrams — you eliminate wrong conclusions in under 5 seconds vs. 25 seconds of diagram work.

patternAll Z are Y → Some Z are Y is Free

A Universal Affirmative (All S are P) always contains its own Particular Affirmative (Some S are P) as a sub-case. If the statement says "All Z are Y," the conclusion "Some Z are Y" is always valid — it is just a weaker version of the same statement.

Step count: Standard approach requires checking the chain — 4 steps. This pattern recognition: 1 step. Use this whenever you see an "All" statement and a "Some" conclusion with the same pair.

eliminationThe Possibility Filter

For possibility conclusions: ask one question — "Do the combined statements produce a definite NEGATIVE about this pair?" If yes, the possibility is impossible. If no (or the statements are silent), the possibility is valid.

Worked example: "No restaurant is a boutique. All buildings are shops. Some shops are boutiques." Does "Some restaurants being buildings is a possibility" follow? Check: is there a definite "No restaurant is a building" conclusion? The statements connect restaurants to boutiques (negatively) but not directly to buildings. No definite negative about restaurants-buildings → possibility is valid. Time saved vs. full diagram: 15 seconds.

patternConversion Before Chain — Always

When a conclusion seems to not follow from the chain rule, try converting one of the statements first, then recheck the chain.

Worked example: "Some C are B. All C are D." You need to check "Some D are B." Direct chain: middle term is C, but the "Some" is in the wrong direction. Convert "All C are D" first — no, you cannot get All D are C. Instead, apply the rule: Some C are B + All C are D → Some D are B (because the "Some" links C to both B and D, so some D must be B). This avoids wasted diagram time — 3 steps vs. 10 steps of Venn drawing.


Fast-Solving Framework

In the exam hall, follow this sequence for every Statement & Conclusions question:

Step 1 — Tag each statement. Write A (All), E (No), I (Some), O (Some not) next to each statement. Takes 5 seconds.

Step 2 — For each conclusion, first try direct conversion. Is the conclusion simply a converted version of one of the statements? If yes, apply the AEIS rule. (A→I, E→E, I→I, O→X). If it converts cleanly, the conclusion follows.

Step 3 — If conversion doesn't work, try the chain rule. Identify the middle term. Use the chain rules: if both are I-type, there is no conclusion about the extremes. If one is All and one is Some (with Some first), you get Some. If one is No and one is All, you get No.

Step 4 — For possibility conclusions: Check only whether a definite negative exists. If no definite negative — possibility follows. If yes — it does not.

Step 5 — When genuinely stuck on a three-statement question, draw a Venn diagram. But do this last, not first.

Flag and skip anything taking over 90 seconds. Come back with fresh eyes.


Solved PYQs

Why this question: This is the most common pattern — two Universal/Particular Affirmatives sharing a middle term. Tests whether you can apply conversion correctly without over-concluding.

Previous Year Questionपिछले वर्ष का प्रश्न2017
Statement: I. All players are Singers. II. All Dancers are Singers. Conclusion: I. Some Singers are Dancers. II. Some Dancers are Players.
  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Both conclusion I & II follow.
  4. Neither conclusion I nor II follows.
Solutionसमाधान
From 'All Dancers are Singers,' by conversion 'Some Singers are Dancers' (Conclusion I follows). Conclusion II ('Some Dancers are Players') cannot be established because there is no direct link between Dancers and Players in the given statements. Only Conclusion I follows.

Solving path: Statement II says "All Dancers are Singers" (A-type). Converting: "Some Singers are Dancers" — that is Conclusion I. Valid. Now for Conclusion II — "Some Dancers are Players" — you need a link between Dancers and Players. Statement I gives you "All Players are Singers" and Statement II gives "All Dancers are Singers." Both groups end up in Singers, but there is no bridge directly connecting Dancers to Players. The middle term (Singers) appears as the predicate in both — this is an undistributed middle. No conclusion about Dancers-Players. Only Conclusion I follows.


Why this question: Three statements with a chain plus a conversion. Tests whether you can handle multiple operations without losing track.

Previous Year Questionपिछले वर्ष का प्रश्न2019
Statements: I. No A is B. II. All C are D. III. Some C are B. Conclusions: I. Some D are B. II. Some B are C. III. All C are B.
  1. Both conclusions I and II follow.
  2. Only conclusion II follows.
  3. Only conclusion III follows.
  4. Both conclusions I and III follow.
Solutionसमाधान
From 'Some C are B' and 'All C are D,' some D are B (Conclusion I follows). From 'Some C are B,' by conversion 'Some B are C' (Conclusion II follows). Conclusion III ('All C are B') is an overstatement not supported. Both Conclusions I and II follow.

Solving path: For Conclusion I — "Some D are B." Look at "Some C are B" and "All C are D." Middle term is C. Some C are B (I-type) + All C are D (A-type). The rule: Some [middle] are [X] + All [middle] are [Y] → Some Y are X. So Some D are B. Conclusion I follows. For Conclusion II — "Some B are C." Convert "Some C are B" (I-type): "Some B are C." Direct conversion. Conclusion II follows. Conclusion III says "All C are B" — that is an overstatement; you only know "Some C are B." Both I and II follow.


Why this question: Two I-type statements. Classic "Some+Some = Dead End" test.

Previous Year Questionपिछले वर्ष का प्रश्न2019
Statements: I. Some red are rat. II. Some rat are wild. Conclusions: I. Some wild are rat. II. All wild are rat. III. Some red are wild.
  1. None of the conclusions follows.
  2. Only conclusion III follows.
  3. Only conclusion I follows.
  4. Only conclusion II follows.
Solutionसमाधान
From 'Some rat are wild,' by conversion 'Some wild are rat' (Conclusion I follows). Conclusion II is an overgeneralization. Conclusion III cannot be established as there's no direct link between red and wild established by the two 'Some' statements. Only Conclusion I follows.

Solving path: Statement II: "Some rat are wild" (I-type). Convert directly: "Some wild are rat." That is Conclusion I. Valid. Conclusion II says "All wild are rat" — you cannot strengthen Some to All without more evidence. Conclusion III says "Some red are wild" — needs a link between red and wild. Statement I gives "Some red are rat" and Statement II gives "Some rat are wild." Middle term is rat, but both are I-type → Some+Some → no conclusion about red and wild. Only Conclusion I follows.


Why this question: Tests your understanding of when a conclusion directly contradicts another.

Previous Year Questionपिछले वर्ष का प्रश्न2020
Statements: 1. Some instruments are machines. 2. All instruments are gadgets. Conclusions: I. No machine is a gadget II. Some machines are gadgets.
  1. Either conclusion I or conclusion II follows
  2. Only conclusion I follows
  3. Neither conclusion I nor conclusion II follows
  4. Only conclusion II follows
Solutionसमाधान
From 'Some instruments are machines' and 'All instruments are gadgets,' some machines are gadgets (Conclusion II follows). Conclusion I directly contradicts this. Only Conclusion II follows.

Solving path: "Some instruments are machines" (I) + "All instruments are gadgets" (A). Middle term is instruments. Rule: Some instruments are machines + All instruments are gadgets → Some machines are gadgets. Conclusion II follows. Conclusion I says "No machine is a gadget" — this directly contradicts Conclusion II. You cannot have both. Since Conclusion II is established as valid, Conclusion I cannot hold. Only Conclusion II follows.


Why this question: Introduces the "possibility" conclusion type — a newer SSC pattern that trips up unprepared candidates.

Previous Year Questionपिछले वर्ष का प्रश्न2020
Statements: 1. All buildings are shops. 2. Some shops are boutiques. 3. No restaurant is a boutique. Conclusions: I. Some boutiques are buildings. II. Some restaurants being buildings is a possibility. III. No restaurant is a shop.
  1. Only conclusion II follows
  2. Only conclusions II and III follow
  3. Only conclusion I follows
  4. Only conclusions I and II follow
Solutionसमाधान
From the given statements, the boutiques that are shops may or may not be buildings — we cannot definitively say some boutiques are buildings (Conclusion I is not certain). No restaurant is a boutique, but restaurants could still be shops, so Conclusion III is too strong. Since restaurants are not established as boutiques or buildings, some restaurants could possibly be buildings (Conclusion II is a possibility). Only Conclusion II follows.

Solving path: Three statements. Conclusion I: "Some boutiques are buildings." From "All buildings are shops" and "Some shops are boutiques" — middle term is shops. All buildings are shops (A) + Some shops are boutiques (I, with Some in the predicate position) → No definite conclusion. The boutiques that are shops may not be buildings. Conclusion I is uncertain. Conclusion III: "No restaurant is a shop." From "No restaurant is a boutique" — this only blocks restaurants from boutiques, not from shops. Too strong. Conclusion II: "Some restaurants being buildings is a possibility." Is there a definite statement that no restaurant is a building? No. So the possibility holds. Only Conclusion II follows.


Why this question: Another Some+Some trap — tests whether you will incorrectly chain two I-type statements.

Previous Year Questionपिछले वर्ष का प्रश्न2021
Statements: Some tablets are laptops. Some laptops are computers. Conclusions: I. Some tablets are computers. II. Some laptops are not tablets.
  1. Neither conclusion I nor II follows
  2. Both conclusions I and II follow
  3. Only conclusion II follows
  4. Only conclusion I follows
Solutionसमाधान
Two 'Some' statements do not establish a definite link between tablets and computers (Conclusion I cannot be established). Conclusion II ('Some laptops are not tablets') is also not provable — it may or may not be the case. Neither conclusion definitively follows.

Solving path: "Some tablets are laptops" (I) + "Some laptops are computers" (I). Two I-type statements with middle term laptops. Some+Some → no definite conclusion about tablets and computers. Conclusion I does not follow. Conclusion II: "Some laptops are not tablets." Is this provable? "Some tablets are laptops" means some laptops are tablets (by conversion). But that does not mean ALL laptops are tablets — so it is possible some are not. However, "possible" is not the same as "definite." You cannot conclude it definitely follows. Neither conclusion follows.


Why this question: Tests whether you will be tempted to fabricate a relationship between terms that only share a third term indirectly.

Previous Year Questionपिछले वर्ष का प्रश्न2021
Statements: I. Some blue are red. II. Some green are red. Conclusions: I. No blue is green. II. No red is green.
  1. Only conclusion I follows
  2. Neither conclusion I nor II follows
  3. Only conclusion II follows
  4. Both conclusions I and II follow
Solutionसमाधान
The statements only establish that some blue are red and some green are red, but provide no information about the relationship between blue and green directly, nor do they exclude green from red. Neither Conclusion I nor Conclusion II can be established from the given statements.

Solving path: "Some blue are red" and "Some green are red." Both are I-type with middle term red in the predicate. Some+Some → no conclusion about blue and green. Conclusion I: "No blue is green" — you have zero information about the blue-green relationship. Cannot conclude a No-statement from silence. Conclusion II: "No red is green" — Statement II says "Some green are red," convert it to "Some red are green," which directly contradicts this. Conclusion II is false. Neither follows.


Why this question: Tests conversion of a Universal Affirmative and the limits of what you can conclude from "All."

Previous Year Questionपिछले वर्ष का प्रश्न2022
Statements: I. All Z are Y. II. Some Y and B. Conclusion: I. Some B are not Z. II. Some Y are not Z. III. Some Z are Y.
  1. Both conclusions II and III follows
  2. All conclusion follows.
  3. Only conclusion III follows
  4. Both conclusions I and III follows
Solutionसमाधान
From 'All Z are Y,' by conversion 'Some Z are Y' (Conclusion III follows). Conclusions I and II cannot be firmly established from the given statements. Only Conclusion III follows.

Solving path: Statement I: "All Z are Y" (A-type). Convert: "Some Y are Z" — and also note that "All Z are Y" directly contains "Some Z are Y" as a particular sub-case. Conclusion III: "Some Z are Y" — this is just a weaker version of Statement I. Directly valid. Conclusion I: "Some B are not Z" — you would need a definite link between B and Z. Statement II gives "Some Y and B" (Some Y are B). From "All Z are Y" you get Some Y are Z. Can you conclude Some B are not Z? Not definitely — it is possible all B that are Y are also Z. Cannot establish. Conclusion II: "Some Y are not Z" — from "All Z are Y," all Z are within Y, but Y might have members outside Z. However, this is possible, not definite. Only Conclusion III follows.


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