Syllogism
🔒 Log in to trackSyllogism questions hand you 2-3 statements (All / No / Some / Some-not / Only-a-few) as true and ask which conclusions follow. The reliable method is minimal-diagram plus counter-example hunting: draw the least-committal picture, then try to break each conclusion — a conclusion follows only if no valid diagram breaks it. Modern twists (possibility conclusions, either-or complementary pairs, 'only a few') all reduce to the same discipline with one twist: possibility needs just one supporting diagram, and either-or needs the two conclusions to be exact negations.
One page per subtopic: detailed notes, every question type, formulas, tricks and practice sets.
Every formula on one printable page, grouped by subtopic.
4 exam-level questions worked step by step.
50 questions — untimed practice or a timed test with analysis.
Track record in the exam
Questions per shift in recent SSC CGL papers.
Test difficulty mix (50 questions)
Question patterns exams keep repeating
Taken from previous-year papers. If a pattern is marked "very common", expect to see it in your exam.
Two-statement definite
very commonTwo statements (an All and a Some/No in some order) with two conclusions about the outer terms.
How to solve: Draw the least-committal diagram, then hunt one counter-diagram per conclusion. The Some-member travels through an All; a No statement exiles it. Reject every conclusion a single moved diagram can break.
Example: Some dogs are cats. All cats are rats. Conclusions: I. Some dogs are rats. II. All rats are dogs.
The dog-cat member is a rat → I follows. Rats spread beyond dogs → II fails. Only I.
Three-statement chain
commonThree statements, usually two All's and one Some/No, with conclusions that need the whole chain.
How to solve: Chain the All-links first (A⊂B⊂C), place the Some/No member last, and trace the guaranteed member through every statement it meets before judging any conclusion.
Example: All keys are locks. Some locks are doors. No door is a window. Conclusions: I. Some keys are doors. II. Some locks are not windows.
The lock-door overlap can dodge keys → I fails. That door-lock is never a window → II follows. Only II.
Possibility conclusion
very commonAny conclusion ending in 'is a possibility'.
How to solve: Build ONE diagram where the possibility holds alongside every statement. It fails only when a guaranteed member would be forced into a forbidden (No) class. Definite and possibility use opposite standards — never mix them.
Example: All roads are streets. Some streets are lanes. Conclusion: All lanes being roads is a possibility.
Draw lanes inside roads, roads inside streets, extra streets outside → consistent → follows.
Either-or complementary pair
very commonNeither conclusion follows alone but the pair is (All, Some-not) or (Some, No) about the same two terms.
How to solve: Check the shape first, then test each conclusion alone — if either follows by itself, pick it. Only a true negation pair with no individual proof earns 'Either I or II follows'.
Example: Some flowers are red. No flower is blue. Conclusions: I. All flowers are red. II. Some flowers are not red.
Neither is provable and the pair is exact negation → Either I or II follows.
Only-a-few statements
common'Only a few A are B' — the modern quantifier.
How to solve: Rewrite as Some A are B + Some A are not B. The A-side split is guaranteed; the B-side is free. Chain only the overlap member through All statements; never chain the outside member.
Example: Only a few cups are plates. All plates are bowls. Conclusions: I. Some cups are not plates. II. No cup is a bowl.
I is guaranteed → follows. Plate-cups are bowls and non-plate cups may be bowls → II fails. Only I.
Conversion-based conclusion
occasionalThe correct conclusion is a reversal: Some B are A from All A are B, or swapped Some/No.
How to solve: Recall the free conversions — All→Some, Some↔Some, No↔No — before rejecting a conclusion as 'reversed'. The only illegal reversal is All B are A.
Example: All roses are flowers. Conclusion: Some flowers are roses.
All→Some conversion always holds (no class is empty) → follows.
Counter-example hunt
commonA conclusion that looks natural but rests on drawing the picture you want.
How to solve: Ask of every conclusion: can I move a free part of the diagram — push an overlap aside, extend a circle — while all statements stay true? One success rejects it. Follows only when no movement can break it.
Example: Some spoons are forks. Conclusion: Some spoons are not forks.
Draw all spoons inside the overlap — statements hold, conclusion breaks → does not follow.
Possibility blocked by a No statement
commonA possibility question whose statements include 'No X is Y' near the possibility's terms.
How to solve: Trace the member guaranteed by a Some or only-a-few statement. If drawing the possibility would push that member into the forbidden class, the possibility is impossible; otherwise it follows.
Example: Some phones are cameras. No camera is a charger. Conclusion: All phones being chargers is a possibility.
The phone-camera member can never be a charger → does not follow.