Syllogism for SSC MTS — All Some None Conclusions Explained

intermediate 18 min read

Concept

Syllogism is a form of deductive reasoning where you are given two or more statements and asked whether certain conclusions can be drawn from them — treating those statements as absolutely true, regardless of real-world facts.

Here is the key mindset shift: you are not testing common sense, you are testing logical validity. If the paper says "All cats are dogs," you accept that. Your job is only to check whether the conclusion follows from the given statements, not whether it matches reality.

Look at a simple example. Suppose you are told:

You can safely conclude: All A are C. Why? Because every A sits inside B, and B itself sits inside C. So A is automatically inside C too.

A good analogy is Russian nesting dolls (матryoshка). If the smallest doll fits inside the medium doll, and the medium doll fits inside the large doll, then the smallest doll is definitely inside the large doll. That is syllogism in one image.

Now for SSC MTS, the statements use one of four types of propositions:

| Type | Statement Form | Symbol used by teachers | |------|---------------|------------------------| | Universal Positive | All A are B | A+ | | Universal Negative | No A is B | E | | Particular Positive | Some A are B | I | | Particular Negative | Some A are not B | O |

You will almost never see "Some A are not B" in SSC MTS Reasoning — the paper favors A+, E, and I. But recognize it when it appears.

The exam gives you 2–3 statements and 2 conclusions. Your answer choices are always: only I follows, only II follows, both follow, neither follows. You have to apply strict logic, not intuition.


Deep Dive

The Four Proposition Types and Their Converses

Before combining statements, you need to know which propositions can be "converted" — that is, flipped — and what form they take after flipping.

All A are B → converts to Some B are A (not "All B are A") This is the single most tested conversion rule in SSC MTS. The direction of "All" cannot be reversed without weakening it to "Some."

No A is B → converts to No B is A (exact reversal is valid for No-statements)

Some A are B → converts to Some B are A (exact reversal is valid for Some-positive)

Some A are not B → does NOT convert to a simple form. Don't attempt it.

The Three Combining Rules (What You Actually Need)

When two statements share a common term (the middle term), you combine them to get a conclusion. Here are the three valid patterns that appear in SSC MTS:

Rule 1: All + All → All

Rule 2: All + No → No

Rule 3: Some + All → Some

The Dead-End Combinations (No Definite Conclusion)

These combinations are the traps the paper uses repeatedly:

The Venn Diagram Method vs. The Rule-Based Method

Two approaches exist. For SSC MTS, the rule-based method is faster for standard questions. Venn diagrams help only when the question has three statements or when you are unsure.

Rule-based method: Identify the middle term (the term shared between the two statements). Combine using the rules above. Check the conclusion against the result.

Venn diagram method: Draw circles for each category. Shade or mark overlaps. Check whether every possible valid diagram satisfies the conclusion. If even one valid diagram breaks the conclusion, it does not follow.

Here is when to use which:

The Conversion Trap

The most commonly missed conclusion type is the reverse-of-All case.

Given: "All pens are cups." Conclusion: "Some cups are pens." — This is VALID. Why? Because "All A are B" converts to "Some B are A."

Many students mark this wrong because it feels like a new claim. It is not. It is a standard conversion. The paper tests this directly (see PYQ 6a2e8a234952599e759b41ed).

Complementary Pairs

Sometimes the paper offers two conclusions that together cover all possibilities — one positive, one negative — and asks you to tick both if at least one must be true. This is called a complementary pair. For SSC MTS, complementary pairs appear rarely, but recognize this structure: if Conclusion I says "Some A are B" and Conclusion II says "No A is B," and neither can be definitively proved or disproved, then both together are complementary and the answer is "either I or II follows." Watch for this when you see "either...or" in the options.


Memory Tricks & Shortcuts

patternNo+No = Dead End

Whenever both statements use "No," the answer is almost always "Neither conclusion follows." The No+No combination cannot produce any definite positive or negative conclusion about the non-middle terms. Standard method: draw Venn diagram (40 seconds). Shortcut: spot the No+No pattern instantly, mark "neither," move on (5 seconds). This pattern appeared in SSC MTS 2024 at least twice — it is a deliberate repeat trap.

patternAll-converts-to-Some (not All)

Before evaluating any conclusion, write out the conversion of each All-statement. "All A are B" always converts to "Some B are A." This prevents the classic error of rejecting a valid "Some B are A" conclusion when "All A are B" is given. Standard method: re-read and reason from scratch (30 seconds). Shortcut: do the conversion as a reflex at the start of every question, then just match conclusions to your conversion list (8 seconds per conclusion check). Step difference: 4 steps vs. 1 step.

patternSome+All Chain — Chase the Middle Term

In a Some+All chain, always check which term is the middle term (appears in both statements). If the middle term is the predicate of the first statement and the subject of the second, the chain fires. Example: "Some A are B. All B are C." Middle term = B (predicate in S1, subject in S2). Chain fires → Some A are C. If the chain order is reversed — "All B are C. Some A are B" — it still fires, just reorder mentally. Standard method: draw Venn (35 seconds). Shortcut: identify middle term and fire the Some+All rule directly (10 seconds). This collapses 3 diagram steps into 1 mental check.

eliminationThe Reversal Test for No-statements

For any conclusion that starts with "No," first check whether the original statements contain a valid All+No or No+All chain pointing toward that conclusion. If the two given No-statements do not share a correctly placed middle term in a productive chain, the "No conclusion" is invalid. Eliminate it immediately. You do not need to draw a diagram. Standard method: attempt Venn diagram construction (40 seconds). Shortcut: check if the chain is No+No (dead end) or All+No/No+All (valid) in 5 seconds, then decide. Saves 35 seconds per such question.

eliminationSome+Some Trap — Always Invalid in SSC

If both statements are "Some," no definite conclusion about the non-shared terms can be drawn. Immediately eliminate any conclusion that claims a definite positive or negative relationship between the outer terms. This is a guaranteed wrong conclusion. Standard method: attempt diagram (30 seconds). Shortcut: see Some+Some, mark "neither" for any conclusion about the outer terms, move on (6 seconds). Four-step saving.


Fast-Solving Framework

In the exam hall, work through each syllogism question in this order:

Step 1 — Identify the middle term. Which term appears in both statements? Circle it.

Step 2 — Check the statement types. Are they All+All, All+No, Some+All, No+No, or Some+Some?

Step 3 — Apply the pattern rule instantly:

Step 4 — Check each given conclusion against your derived conclusion AND the conversions of your given statements. Remember: "All A are B" gives you "Some B are A" for free.

Step 5 — Mark and move. Do not second-guess. If the pattern says neither, mark neither. Real-world logic has no role here.

Target time: 25–35 seconds per question. If you are going beyond 45 seconds, you are reasoning from intuition instead of rules — reset and apply the framework.


Solved PYQs

Why this question: Tests the most fundamental All+All chain and the All-converts-to-Some rule simultaneously. If you understand this one, you understand the core of syllogism.

Previous Year Questionपिछले वर्ष का प्रश्न2017
Statements: I. All pens are cups. II. All cups are chairs. Conclusions: I. All pens are chairs. II. Some cups are pens.
  1. Both conclusions follow.
  2. Neither conclusion (I) nor conclusion (II) follows.
  3. Only conclusion (I) follows.
  4. Only conclusion (II) follows.
Solutionसमाधान
From 'All pens are cups' and 'All cups are chairs', it follows that all pens are chairs (Conclusion I). Also, since all pens are cups, some cups must be pens (Conclusion II). Both conclusions are valid.

Solving path:


Why this question: The No+No dead-end trap. This is the question SSC MTS has reused across multiple years — 2024 had two versions of the same scenario.

Previous Year Questionपिछले वर्ष का प्रश्न2024
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, decide which of the given conclusions logically follow(s) from the statements. Statements: No soap is a lotion. No lotion is a conditioner. Conclusions: (I) No soap is a conditioner. (II) Some conditioners are lotions.
  1. Only conclusion I follows
  2. Neither conclusion I nor II follows
  3. Only conclusion II follows
  4. Both conclusion I and II follow
Solutionसमाधान
From 'No soap is a lotion' and 'No lotion is a conditioner', we cannot definitively conclude that no soap is a conditioner (there may be other connections), and conclusion II contradicts the second statement. Hence neither conclusion follows.

Solving path:


Why this question: Tests whether students incorrectly assume that "All lizards are reptiles" means all reptiles must be lizards — a classic reversal error.

Previous Year Questionपिछले वर्ष का प्रश्न2024
Read the given statement(s) and conclusions carefully. Assuming that the information given in the statements is true, decide which of the given conclusions logically follow(s) from the statement(s). Statements: No lizard is a snake. All lizards are reptiles. Conclusions: (I) At least some reptiles are snakes. (II) All reptiles are lizards.
  1. Only conclusion (II) follows
  2. Neither conclusion (I) nor (II) follows
  3. Both conclusions (I) and (II) follow
  4. Only conclusion (I) follows
Solutionसमाधान
Since lizards and snakes are separate groups within reptiles, we cannot say some reptiles are snakes (conclusion I is invalid), and reptiles can include non-lizards (conclusion II is also invalid). Neither follows.

Solving path:


Why this question: Confirms the Some-converts-to-Some rule and the No-statement blocking rule in one question.

Previous Year Questionपिछले वर्ष का प्रश्न2024
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements. Statements: Some cameras are phones. No phone is a laptop. Conclusions: (I) Some phones are cameras. (II) Some laptops are phones.
  1. Both conclusion I and II follow
  2. Only conclusion II follows
  3. Neither conclusion I nor II follows
  4. Only conclusion I follows
Solutionसमाधान
From 'Some cameras are phones,' it directly follows by conversion that 'Some phones are cameras' (Conclusion I is true). Since no phone is a laptop, no laptops can be phones, so Conclusion II is false.

Solving path:


Why this question: A three-statement question where the Some+Some trap appears. Students often draw a chain through all three statements and land on a wrong conclusion.

Previous Year Questionपिछले वर्ष का प्रश्न2023
Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. You have to decide which conclusion/s logically follow/s from the given statements. Statements: All rags are carpets. Some carpets are steel. Some steel are bottles. Conclusion I: All carpets are rags. Conclusion II: Some carpets are bottles.
  1. Neither conclusion (I) nor (II) is follow.
  2. Only conclusion (I) is follow.
  3. Both conclusions (I) and (II) are follow.
  4. Only conclusion (II) is follow.
Solutionसमाधान
Conclusion I is invalid because 'All rags are carpets' doesn't mean all carpets are rags. Conclusion II cannot be established since 'some carpets are steel' and 'some steel are bottles' doesn't guarantee overlap between carpets and bottles.

Solving path:


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