Syllogism is, at its core, a formal system for drawing conclusions from a set of given statements — and doing it without letting your real-world knowledge interfere. That last part is where most aspirants slip up.
Here is the mental model that works: treat every syllogism question as if you are an alien who has just landed on Earth and knows nothing about pens, mangoes, or birds. You only know what the statements tell you. If a statement says "All pens are chairs", you accept it as gospel truth inside the exam question, regardless of what you know about pens.
The core vocabulary:
Think of it like a map. "All A are B" means the circle for A is drawn entirely inside the circle for B. "No A is B" means the two circles do not touch. "Some A are B" means the circles overlap, but you do not know by how much.
The analogy that works in the classroom: imagine you are filling water into containers. "All A are B" means every drop of water in container A has already been poured into container B. "No A is B" means the two containers are on opposite sides of the room — not a single drop is shared.
SSC CGL typically gives you two or three statements and asks which of the given conclusions necessarily follow. The word necessarily is everything. A conclusion must be true in all possible valid Venn diagram arrangements, not just one of them.
| Statement Type | Notation | What is guaranteed | |---|---|---| | All A are B | Universal Positive | Every A is in B. Some B may or may not be A. | | No A is B | Universal Negative | Zero overlap. This is reversible: No B is A is also valid. | | Some A are B | Particular Positive | At least one A is B. Reversible: Some B are A is also valid. | | Some A are not B | Particular Negative | At least one A is outside B. Not reversible. |
Conversion rules — these are the most useful rules to memorise:
The real skill is chaining two statements together to get a valid conclusion.
Chain 1: All + All → All
Chain 2: All + No → No
Chain 3: Some + All → Some
Chain 4: Some + No → Some...not
Chain 5: All + Some → Some (weak side)
This last one is a classic trap. Just because all A are B, and some B are C, you cannot say "Some A are C" — because the B that overlaps with C might be the part of B that is not A.
Chain 6: No + Some → Some...not
SSC CGL sometimes asks about "possibility" conclusions, phrased as "It is possible that some A are B." A possibility conclusion is valid if it does not contradict the given statements. Even if the conclusion does not definitely follow, if it is consistent with at least one valid Venn diagram arrangement, the possibility holds.
When you see "possibility" in a conclusion, your question changes from "Does this necessarily follow?" to "Can this be true without breaking any statement?"
In the exam hall, you do not always have time to draw full diagrams. Here is the mental shortcut:
For three-statement questions: chain the first two, get an intermediate conclusion, then chain that with the third statement.
"No A is B" is the only universal statement that converts symmetrically — "No B is A" is always valid with the same certainty. Remember: No flips Neatly. Every other universal ("All A are B") loses strength when converted. Standard approach: verifying conversion case-by-case = 20 seconds per question. Using ANNA Rule: 3 seconds — spot "No" in conclusion, immediately check if it is the reverse of a "No" statement.
When chaining two statements, the conclusion is always at most as strong as the weaker statement. If either statement contains "Some", your conclusion will contain "Some" (not "All"). If either is negative ("No" or "Some...not"), your conclusion will be negative. Standard approach: drawing all combinations to find conclusion strength = 40 seconds. Weak Link Principle: categorise each statement (universal/particular, positive/negative), pick the weaker label, derive conclusion type in under 10 seconds.
In a three-statement chain, one term will appear only once across all statements — the "orphan". A valid conclusion must connect two terms that are actually linked through the chain. If a conclusion mentions the orphan term paired with another term that has no chain connecting them, eliminate that conclusion immediately without any calculation. This eliminates at least one wrong conclusion in roughly 5 seconds vs. 25 seconds of full diagramming.
"Some A are B" + "All B are C" → "Some A are C". This chain always works because every B is inside C, so the A-members that are B must also be in C. However, "All A are B" + "Some B are C" gives NO conclusion about A and C — the "Some" is on the wrong side. Remember the direction: Some on the left of All chains forward. Spotting this saves you from the most common wrong answer in SSC CGL syllogism sets — aspirants mark "Some A are C" even when Some is on the right side of All, costing roughly 2-3 marks per paper.
"No A is B" + "All B are C" does NOT give "No A is C". Many aspirants assume it does. The correct chain is: since all B are C, and no A is B, some C (specifically the C that came from B) are not A. Remember: No + All gives Some...not, not another No. Standard trap: choosing "No A is C" in the answer = wrong answer. Correct derivation takes 15 seconds; knowing this rule takes 3 seconds.
In the exam hall, follow this decision tree for every syllogism question:
Step 1 — Read all statements, label each (U+, U−, P+, P−) where U = Universal, P = Particular, + = Positive, − = Negative. Takes 10 seconds.
Step 2 — Identify the link term (appears in two statements). Write the chain mentally: Statement 1 links to Statement 2 via the link term.
Step 3 — Apply chain rule from the table above. Get your derived conclusion.
Step 4 — Check each given conclusion:
Step 5 — For "No" conclusions, always verify by checking if it is the valid conversion of a "No" statement in the chain. Do not accept "No X is Y" unless you can point to a "No Y is X" or directly derive it.
Total target time per syllogism question: under 60 seconds.
Why this question: This is the classic three-statement set testing whether you chase a "No" conclusion too aggressively. The trap is Conclusion II.
Solving path: Link "No pen is pencil" with "All pencils are stationery". Use the Some...not chain: since all pencils are stationery and no pen is a pencil, some stationery (the pencil portion) are not pens — Conclusion III follows. For Conclusion I: we know some stationery are expensive, but we cannot place pencils inside the expensive portion — no valid chain connects "expensive" to "pencils". For Conclusion II: "No pen is stationery" would require all stationery to come from pencils, which is not stated — pens could be other types of stationery. Answer: Only III.
Why this question: Tests the critical Some + All chain, and whether you incorrectly extend "All books are pages" + "Some pages are words" to claim "Some books are words".
Solving path: Statement 1: All books are pages. Statement 2: Some pages are words. Here "Some" is on the right side of All — no conclusion about books and words follows (I is false). Now chain Statement 2 and Statement 3: Some pages are words + No word is a letter → Some pages are not letters (P+ + U− → P− chain). Conclusion III follows. Conclusion II says "No page is a letter" — that is a universal negative, but we only derived "some pages are not letters" — far weaker. Answer: Only III.
Why this question: Tests the Some + All forward chain, and whether "No car is bike" + "Some useful things exist" lets you conclude "No car is useful".
Solving path: Chain Statement 2 and Statement 3: Some bikes are vehicles + All vehicles are useful → Some bikes are useful (I is true — valid Some + All forward chain). Now Conclusion II claims no car is useful. The statements tell you no car is a bike, but cars could be useful through other means not mentioned. No valid chain eliminates car from useful. Conclusion III: some useful things are not cars — since some bikes are useful and no car is a bike, some useful things (those bikes) are definitely not cars. III follows. Answer: Only I and III.
Why this question: Near-identical structure to the car-bike question above, but with birds-fish-sharks. Many aspirants rush to mark "No bird is dangerous" because of the "No bird is fish" statement.
Solving path: Chain Statement 2 and Statement 3: Some fish are sharks + All sharks are dangerous → Some fish are dangerous (II is true). Now Conclusion I: "No bird is dangerous" — we know no bird is a fish, but danger can come from being a shark, or from other sources entirely. The statements give no information ruling out birds from being dangerous. I does not follow. Conclusion III: some dangerous things are not birds — since some fish are dangerous and no bird is a fish, those dangerous fish are definitely not birds. III follows. Answer: Only II and III.
Why this question: This question specifically isolates the "All + Some on wrong side" trap for Conclusion I, and the "All + Some + No chain for Some...not" for Conclusion III.
Solving path: Statement 1: All computers are machines. Statement 2: Some machines are fast. "Some" is on the right of All — no conclusion about computers and fast. Conclusion I is false. Conclusion II: No computer is slow — for this we would need to chain computers to fast, which we cannot. Computers might not be the fast machines. Conclusion II is false. Statement 2 + Statement 3: Some machines are fast + No fast thing is slow → Some machines are not slow. Conclusion III is true. Answer: Only III.
Applying real-world knowledge. If the statement says "All dogs are cats", you accept it. The moment you think "but that is impossible", you are reasoning outside the question — and you will get the answer wrong.
Converting "All A are B" to "All B are A". This is invalid. You can only convert it to the weaker "Some B are A". Choosing a conclusion that says "All B are A" based on "All A are B" is a guaranteed wrong mark.
Accepting "No A is C" from "No A is B" + "All B are C". Look at the PYQ on computers above. The correct chain is "Some C are not A" — a particular negative, not a universal negative. Do not upgrade the conclusion.
Treating "Some A are B" + "All B are C" as symmetric — i.e., assuming "All A are B" + "Some B are C" also gives "Some A are C". It does not. The chain only works when "Some" is on the left (subject side) of the All statement.
Ignoring the conversion of "Some A are B" to "Some B are A". Conclusions are sometimes written as the valid conversion of what you derived. If you derived "Some B are A" but the conclusion says "Some A are B", it still follows — they are equivalent.
Missing the "Some...not" conclusion from No + All or No + Some chains. Aspirants often look for definite "No" or "Some" conclusions and ignore that a "Some...not" conclusion is often the correct and only valid result from a negative chain.